Prig losing head becomes unmannerly (4)
I believe the answer is:
rude
'unmannerly' is the definition.
(I know that unmannerly can be written as rude)
'prig losing head' is the wordplay.
'prig' becomes 'prude' (I've seen this before).
'losing head' means to remove the first letter.
'prude' with its initial letter taken away is 'RUDE'.
'becomes' acts as a link.
(Other definitions for rude that I've seen before include "'Bad-mannered, discourteous (4)'" , "Offensive; unpolished" , "Primitive; impolite" , "Offensively impolite" , "Coarse or discourteous" .)