Priggish person (5)
I believe the answer is:
prude
'priggish person' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for prude that I've seen before include "One is excessively concerned with propriety and decorum" , "Mrs Grundy type" , "old maid" , "may be shocking for me" , "Easily shocked person" .)