Sons press for big increase (5)
I believe the answer is:
surge
'big increase' is the definition.
'sons press' is the wordplay.
'sons' becomes 's'.
'press' becomes 'urge' ('urge' can be a synonym of 'press').
's'+'urge'='SURGE'
'for' acts as a link.
(Other definitions for surge that I've seen before include "Sudden large increase" , "significant increase" , "Sudden rush" , "Movement in crowd" , "Jerk" .)