What's possible after media persevere (5,2)
I believe the answer is:
press on
'persevere' is the definition.
(to press on is to persevere)
'what's possible after media' is the wordplay.
'what's possible' becomes 'on' ('not on' can mean unacceptable or not possible).
'after' means one lot of letters go next to another.
'media' becomes 'press' (the press is part of the media).
'on' after 'press' is 'PRESS ON'.
(Other definitions for press on that I've seen before include "Hasten insistently" , "Continue going forward" , "don't stop!" , "Continue (with action)" , "Keep going forward" .)