Assuming that you are not restricting this to Roman poets, Alcaeus of Mytilene (circa 625–620 to circa 580 BC), a Greek lyric poet from Lesbos may be of help. He was certainly known to Ovid, who even paid tribute to him through Alcaeus's contemporary Sappho in The Heroides (15):
But the Muses compose the sweetest songs for me:
now, my name is sung throughout the world:
Alcaeus is not more praised, who shares the lyre
and my country, even though he may sound more grand.
While in exile, Alcaeus, in his political songs, covered
the power struggles on Lesbos with the passion and vigour of a
partisan, cursing his opponents, rejoicing in their deaths,
delivering blood-curdling homilies on the consequences of political
inaction and exhorting his comrades to heroic defiance, as in one
of his 'ship of state' allegories. Commenting on Alcaeus as a
political poet, the scholar Dionysius of Halicarnassus once observed
that "...if you removed the meter you would find political
Unfortunately, Alcaeus' work only survives in fragments. These, along with a biography, can be accessed on the Internet Archive site in its copy of The songs of Alcaeus; memoir and text; with literal and verse translations and notes by James S. Easby-Smith (1901). A more recent work, Jan Felix Gaertner's Writing Exile: The Discourse of Displacement in Greco-Roman Antiquity and Beyond (2007) may also prove useful, and not just for the references to Alcaeus.
If you are not restricting this to poets, Ovid was also familiar with Greek playwrights, including Euripides (died around 406 BC), who actually wrote about exile before his own self-imposed exile in Macedonia. Prior to this, though, he spent
many of his later years...living in a cave on Salamis away from
Source: Robert Gorman, 'Poets, Playwrights, and the Politics of Exile and Asylum in Ancient Greece and Rome' (International Journal of Refugee Law, Volume 6, Issue 3, 1994, Pages 402–424)
He was an unpopular figure in his home city of Athens and this, according to Gorman,
may have contributed to the cause of his exile.
He wrote about exile in (among other plays) The Medea, The Heracleidae, and Hippolytus:
The theme of exile, if not born from his own personal experience, is
more prevalent in Euripides' extant works than in those of any other