University pays outsiders to push for a rise (7)
I believe the answer is:
upsurge
'a rise' is the definition.
(I've seen this before)
'university pays outsiders to push' is the wordplay.
'university' becomes 'u' (abbreviation for university).
'outsiders' says to hollow out the word (remove centre letters) (only the letters on the outside of the word remain).
'to push' becomes 'urge' (I've seen this in another clue).
'pays' with its middle removed is 'ps'.
'u'+'ps'+'urge'='UPSURGE'
'for' acts as a link.
(Other definitions for upsurge that I've seen before include "Sudden or abrupt strong increase" , "Hike" , "A sudden rise as in fortunes" , "Sudden rapid increase" , "Rapid rise" .)