Increase in students initially restricted by University clear-out (7)
I believe the answer is:
upsurge
'increase' is the definition.
(upsurge is a kind of increase)
'students initially restricted by university clear-out' is the wordplay.
'initially' says to take the initial letters.
'restricted by' is an insertion indicator (I've seen this in other clues).
'university' becomes 'u'.
'clear out' becomes 'purge' (I've seen this before).
The initial letter of 'students' is 's'.
'u'+'purge'='upurge'
's' going into 'upurge' is 'UPSURGE'.
'in' acts as a link.
(Other definitions for upsurge that I've seen before include "Rapid rise" , "Sudden or abrupt strong increase" , "A sudden rise as in fortunes" , "Sudden rapid increase" , "Effect of groundswell" .)