Puritan losing head becomes vulgar (4)
I believe the answer is:
rude
'vulgar' is the definition.
(vulgar can mean rude or gross)
'puritan losing head' is the wordplay.
'puritan' becomes 'prude' (synonyms).
'losing head' means to remove the first letter.
'prude' with its first letter taken away is 'RUDE'.
'becomes' is the link.
(Other definitions for rude that I've seen before include "Coarse, unpolished" , "Uncivilised" , "Unmannerly" , "Base" , "Insolent" .)