Is there any way to expedite a MBP 2011 discrete GPU failure
My reputation is too low to comment so I am writing it here.

bob gave you wrong information.

If you go to Apple's official page https://www.apple.com/sg/support/macbookpro-videoissues/
it says that


  The program covers affected MacBook Pro models until December 31, 2016 or four years from its original date of sale, whichever provides longer coverage for you.


The longer would be until 2016 December for you.