Question was heavily edited. Answer is therefore now in two parts. The second part actually depends on the first.
1 Original question
Q Was the Hebrew Bible modified after the death of Jesus?
What most would consider the 'Hebrew bible' seems in the context of this question come to mean a Jewish bible, TNK, or from a Christian view, the closely related but not identical 'the Old Testament'.
The text of this compilation is written mostly in Hebrew with a few parts in Aramaic. This text only came into the now seen as 'fixed' form after a hefty few of those events we know as crucifixion of Jesus and destruction of the second temple in Jerusalem at the end of the Jewish war against Rome.
Only then, almost in parallel to the canonisation of the Christian texts we know as the New Testament, the collection of books that were considered 'scripture' were really brought slowly into the form we now find frequently published. That form is the so-called Masoretic text (MT).
We can prove this by looking exactly at the Dead Sea Scrolls, which contain often very similar text versions compared to modern bibles. But also completely other texts that were considered tora (teaching, law), or quite different versions of texts we think we really know from the Masoretic version.
Similarly, the Septuagint, or LXX, an earlier Greek translation from Hebrew shows sometimes remarkable differences from later Masoretic versions. This 'version' probably was never really fixed, but circulating in versions, different from what is now the TNK, and in Greek – and as such most often used by early Christian writers when they were "quoting scripture". The Greek LXX is – from sometimes to often – more properly called the "old Testament" than the modern Jewish Masoretic based Jewish Bible.
Finally, the prime witness of the late first century Josephus tells of the now hopefully very familiar tripartite division of the TNK in T, N and K: Tora, Prophets and Writings. But without telling us what exactly these are, no details on what is in them (although the outline just 'has' to be very close to the familiar one, it just is not easily reconcilable to the Masoretic version) and crucially: he mentions only 22 books, while we would expect them to be 24!
For comparison we need to realise that for example a protestant bible includes as 'Old Testament' one set books and counts them as 39, while Catholic is larger and not only 'counts' 46 and Eastern Orthodox arrives at 49!
Obviously, by his time there was still some flux. Whether they were known by their titles (exact content undetermined), just organised differently (like: were 1 and 2 Chronicles perhaps seen as just 'Chronicles'), or whole books missing (like: is 'Daniel' in or out), all that is uncertain.
Without further qualifications from the question: yes,'the Hebrew bible', while being based on partially vastly older texts compared to the 'time of Jesus', was far from finished, but constantly re-written (example), until the end of the first century AD. From then on it gets a bit murky in terms of source quality and archaeological finds. For a large part the text certainly did not change that much afterwards, but the process the Masoretes forced still took some time. The oldest extant 'full version' is the Aleppo Codex, dated to the 9th/10th century.
The Masoretic version of this collection has to be seen as the one version, that itself solidified quite late and only in the very end really 'won out'.
But changes to that text were appearing until the Middle Ages.
Perhaps the most prominent example: Often the vocalisations chosen by the Masoretes are simply dismissed as 'insignificant'. But the one word for the very name of God יהוה is vocalised to be read out not in any way to really have the letters YHWH in it. Instead this word gets the vocal points for adonai and should be read in Rabbinic Jewish tradition in that way: adonai. While still having the consonants YHWH in it.
Together this results in the naive biblical Hebrew reader to decipher the consonants, add the vowels as pointed, and arrive at the 'non-existing' result of 'Jehovah', which is just incorrect at all levels. Whether to really consider the numerous choices that were made — precisely to take out the ambiguity the consonantal text presented — as insignificant is then another choice. One that is certainly even later.
Wikipedia has a visualisation which is neither chronologically exact noor accounting for inherent plurality of 'scriptures' in 'Qumranic times' (all "lost" simply postulate an intertextual dependency of obscure nature…), but illustrates that the MT-tradition is only coming into a distinct being later:
2 Updated question
Q Was the Hebrew Bible modified and rewritten from Aramaic to Hebrew after the death of Jesus?
Yes. And no.
Apart from the unequivocal 'yes' for the first part: As shown in part one there was not the bible during what we consider the lifetime of Jesus.
There was a collection of writings considered holy for the Jewish sects of the time, pharisees, sadducees, etc. Most of the writings were in Hebrew, some of them written in Aramaic, and some even not only translated into Greek, but also written originally in Greek. 2 Maccabees for example is a 'Jewish' text, now in some 'Old Testaments', originally not in Hebrew but Greek.
As with the reason the Septuagint even exists: many 'Jews' did not really speak fluent Hebrew or used it in everyday communication. Hebrew by that time was almost reserved for scholarship and worship, while most inhabitants used primarily Aramaic. But on top they usually had to know quite a bit of Greek and a bit Latin, being in a Roman province.
That means for most people able to read it we have to assume that practically an Aramaic translations was 'the bible', or the targumim; for many, especially those not being in Palestine, it was Greek. FOr scholarly purposes of original scripture writing, the preferred language was still Hebrew, as we might also conclude from the distribution of languages used in the scrolls found in the caves at the Dead Sea.
As demonstrated in part one, 'the Jewish Bible' most think of today is based on the Masoretic text. This text version was compiled and written by people who largely rejected innovations considered 'late', striving instead to preserve what they perceived as 'more original'. That doesn't always meant preferring 'the oldest, 'most authentic' or 'most original'. It meant primarily: 'prefer Hebrew', 'avoid Aramaic', and 'certainly don't use Greek'. It meant also to reject parts we find in the Septuagint that are most certainly older than the Masoretic version, but for some reason the younger version was preferred. We can't always say for which and there is no clear pattern reconstructable. More beautiful prose/poetry, or better suiting/useful theological content? Some other rationale, like popularity for certain factions, or mere availability?
And even the Hebrew-only texts the Soferim used to produce this MT can be analysed to demonstrate that they re-wrote the texts ever so slightly when a certain phrase was popular/vulgar/'modern' and instead favoured a more archaic, or probably in their eyes 'more exact' rendering.
Taken together: we see that 'at the time of Jesus' there was at best still only a proto-MT to be finalised as 'the one text' collection that eventually won out in a fixed form. What is improbable is to assume that the majority of texts would have been in Aramaic by then, and then rewritten into Hebrew. Hebrew texts even in the proto-MT form were not that sacrosanct as to be free from any changes. Hebrew text forms at the time were certainly seen as having an edge in 'authority' over 'versions' in other languages. But these Hebrew texts were not alone, not fixed and instead to be found in great diversity. Certain groups will have existed for longer that said: "It's only this one text that counts! And that was never and shall never be changed!"
Compare Dtn 4.2:
Ye shall not add unto the word which I command you, neither shall ye take anything from it, that ye may be shomer mitzvot of the commandments of Hashem Eloheichem which I command you.
(and by coincidence, "it's ours!")
That is still true even for the very Torah, the first five books of any bible, the five books of Mose. The Samaritans still say that the Jews got it all wrong and consequently also all Christians, since only they have the true word of God and thus the only Testament.
The great 'authority' of 'one fixed text collection' for either Christians or Rabbinic Judaism came later than 'before the time of Jesus'. Only in the sense of "There was one Aramaic Urtext that was then changed into Hebrew" can we firmly say "no".
Since the discovery of the Qumran scrolls, it has become clear that a unified text tradition before the turn of the eras never existed. In the last centuries B.C.E., a large number of copies of the biblical text, attesting to a large number of different texts, circulated in ancient Israel. Each manuscript constituted an independent entity, since scribes allowed themselves much freedom.
Although the recognition of errors remains subjective, all manuscripts of all texts from antiquity contain errors, including the MT. The very choice in antiquity of the MT as the basis for the biblical text entailed the inclusion of errors in that text.
The fact that the MT contains mistakes does not cause a problem. One can either remove such mistakes in an eclectic edition or translation, or mark them in a multi-column edition. But the existence of mistakes does imply that focusing on the MT is not conducive to a good understanding of the Hebrew Bible as a whole.
— Emanual Tov: "The Status of the Masoretic Text in Modern Text Editions of the Hebrew Bible", in: Lee Martin Mcdonald & James A. Sanders (eds): "The Canon Debate", Hendrickson Publishers: Peabody, 2002.