One losing head, very little girl in a state (6)
I believe the answer is:
nevada
'a state' is the definition.
(Nevada is an example)
'one losing head very little girl' is the wordplay.
'losing head' means to remove the first letter.
'very little' becomes 'v' (abbreviation or little form for 'very').
'girl' becomes 'ada'.
'one' with its first letter taken off is 'ne'.
'ne'+'v'+'ada'='NEVADA'
'in' acts as a link.
(Other definitions for nevada that I've seen before include "US desert state" , "State including Las Vegas" , "See 14" , "Sagebrush State" , "part of US" .)