A loose woman rising in US city (5)
I believe the answer is:
tulsa
'us city' is the definition.
(I've seen this before)
'a loose woman rising' is the wordplay.
'loose woman' becomes 'slut' (synonyms).
'rising' says the letters should be written in reverse (letters written upwards in a down clue).
'a'+'slut'='aslut'
'aslut' backwards is 'TULSA'.
'in' acts as a link.
(Other definitions for tulsa that I've seen before include "An OK place" , "American city" , "Major oil centre" , "Oklahoma city (only 24 hours away?)" , "Oklahoman city" .)