First, a request for rehearing (which must be filed if at all within 14 days) operates as an automatic stay of the suspension. It means that Brady, if a petition for rehearing is filed, would have his suspension held in abeyance until, at the earliest, the Second Circuit decides not to conduct a rehearing and, at the latest, until the rehearing is resolved with another ruling against Brady and the NFLPA.
If the petition for rehearing is granted, a source with knowledge of the Second Circuit procedures tells PFT that it’s quite possible (if not likely) that Brady will be able to play the entire 2016 season, regardless of the outcome.
http://profootballtalk.nbcsports.com/2016/04/25/brady-nflpa-should-definitely-pursue-a-rehearing-before-the-full-second-circuit/