Proper, priggish (4)
I believe the answer is:
prim
This clue is a double definition.
'proper' is the first definition.
(similar in meaning)
'priggish' is the second definition.
(I know that priggish can be written as prim)
(Other definitions for prim that I've seen before include "Old-maidish" , "Stiffly formal and proper" , "Strait-laced - prudish" , "Affectedly formal" , "Proper or prissy" .)