Prudish priest reaching edge (4)
I believe the answer is:
prim
'prudish' is the definition.
('prim' can be a synonym of 'prudish')
'priest reaching edge' is the wordplay.
'priest' becomes 'p' (ecclesiastical abbreviation).
'reaching' is a charade indicator (letters next to each other).
'edge' becomes 'rim' (rim is a kind of edge).
'p'+'rim'='PRIM'
(Other definitions for prim that I've seen before include "Strait-laced - prudish" , "Straitlaced and proper" , "Prudish, proper" , "Proper or prissy" , "Affectedly dainty or refined" .)