Apply to be specialist? No pressure! (5)
I believe the answer is:
exert
'apply' is the definition.
(exerting is a kind of applying)
'be specialist? no pressure' is the wordplay.
'be specialist?' becomes 'expert' (I've seen this before).
'no' is a deletion indicator.
'pressure' becomes 'p' (abbreviation).
'expert' with 'p' removed is 'EXERT'.
'to' is the link.
(Other definitions for exert that I've seen before include "Bring into use, strength or influence" , "Employ" , "Apply (pressure)" , "Bring quality or influence into play" , "Apply (force)" .)