http://www.nfl.com/news/story/0ap3000000674332/article/tom-bradys-appeals-petition-denied-remains-suspended
he's got 90 days to do this:
Quote
if Brady petitions the Supreme Court, his legal team could first ask the Second Circuit Court for a stay of its decision. If the Second Circuit doesn't grant a stay, Brady's lawyers could then request for a stay from the Supreme Court, which would be decided by Justice Ruth Bader Ginsberg. If Ginsberg granted a stay or the court decided to hear the case, Brady almost certainly would be eligible to play the entire 2016 season due the Supreme Court's schedule. Brady would be forced to serve his suspension if the Supreme Court chose not to hear the appeal.
I think he will try