Head girl wanting day off in US capital (7)
I believe the answer is:
raleigh
'us capital' is the definition.
(state capital of North Carolina)
'head girl wanting day off' is the wordplay.
'wanting' is a deletion indicator (to want something can mean to lack it or need it).
'day' becomes 'd' (abbreviation for day).
'off' is an anagram indicator.
'head'+'girl'='headgirl'
'headgirl' with 'd' taken out is 'heagirl'.
'heagirl' is an anagram of 'RALEIGH'.
'in' is the link.
(Other definitions for raleigh that I've seen before include "Favourite of Elizabeth I executed for treason" , "Sir Walter . . . . . . . early tobacco importer" , "Queen's favourite" , "Courtier favourite of Elizabeth I" , "Elizabethan courtier" .)