Pursuing every possibility, despite expectations (5,3)
I believe the answer is:
after all
'despite expectations' is the definition.
(eg 'she went to the party after all')
'pursuing every possibility' is the wordplay.
'pursuing' becomes 'after' (if you're pursuing something you're after it).
'every possibility' becomes 'all' (all possibilities).
'after'+'all'='AFTER ALL'
(Other definitions for after all that I've seen before include "Despite expectations to the contrary" , "I mean, when everything's said and done" , "when push comes to shove" , "When everything is said and done" , "In spite of everything" .)