Girl losing her head, the idiot (3)
I believe the answer is:
ass
'idiot' is the definition.
(both can mean a stupid person)
'girl losing her head' is the wordplay.
'girl' becomes 'lass' (lass can informally mean a girl).
'losing her head' means to remove the first letter.
'lass' with its initial letter removed is 'ASS'.
'the' acts as a link.
(Other definitions for ass that I've seen before include "Hardy and sure-footed animal" , "Animal of horse family" , "One easily had" , "Bottom, temporarily" , "Clinton's behind" .)