Talley has a connection to new Jets HC Todd Bowles, as they worked together a few years ago in Arizona.
Talley, 29, originally signed on with the Green Bay Packers as an undrafted free agent out of Delaware back in 2009. He later caught on with the Cardinals before joining the Buccaneers in June of last year.
The last time Talley appeared in an NFL game was during the 2013 season while he was playing for the Cardinals. During his three seasons in Arizona, he played in 15 games and recorded one sack and 14 tackles.