Prudish, like one sort of minister mostly (4)
I believe the answer is:
prim
'prudish' is the definition.
('prim' can be a synonym of 'prudish')
'one sort of minister mostly' is the wordplay.
'one sort of minister' becomes 'prime'.
'mostly' means to remove the last letter.
'prime' with its final letter removed is 'PRIM'.
'like' acts as a link.
(Other definitions for prim that I've seen before include "Strait-laced - prudish" , "Proper (type of rose?)" , "Stiffly correct" , "Stiffly formal and proper" , "Prudish, proper" .)