Penny's on edge, being prudish (4)
I believe the answer is:
prim
'prudish' is the definition.
('prim' can be a synonym of 'prudish')
'penny's on edge' is the wordplay.
'penny' becomes 'p'.
'on' says to put letters next to each other.
'edge' becomes 'rim' (rim is a kind of edge).
'p'+'rim'='PRIM'
'being' is the link.
(Other definitions for prim that I've seen before include "Demure" , "Affectedly dainty or refined" , "Old-maidish" , "Proper or prissy" , "Straight-laced" .)