I am not referring to the Legati Augusti pro praetores of the Empire.
In republican Rome, provincial governors chose their own legates quite freely.
I found here https://en.wikipedia.org/wiki/Legatus :
a legate could be invested with propraetorian imperium (legatus pro praetore) in his own right
An example of such rank is T. Labienus, legatus pro praetore for Caesar.
My understanding of the wikipedia quote is that the legatus pro praetore is both a legate, acting as a lieutenant for the proconsul, and a fully-empowered provincial magistrate, because he had his own imperium and not just a delegation of the proconsul's.
So could we say the legatus pro praetore is more like the quaestor, a (pro)magistrate under the command of an other promagistrate, or more like the regular legati ?
Could the proconsul "promote" a simple legate by granting him an imperium (I believe he can't) or was the senate involved (the same way it created proconsuls) ?
In the second option, did the senate have a say in the name of the future legatus pro praetore ?
Bonus question : is there any record of a legatus pro praetore serving several governors without returning to civilian life in between, or of a republican legatus pro praetore serving under no governor/consul at all ?