Hospital bill rising in city (4)
I believe the answer is:
bath
'city' is the definition.
(I've seen this before)
'hospital bill rising' is the wordplay.
'hospital' becomes 'h'.
'bill' becomes 'tab' (tab is a kind of bill**).
'rising' says the letters should be written in reverse (going up in a down clue).
'h'+'tab'='htab'
'htab' in reverse letter order is 'BATH'.
'in' acts as a link.
(Other definitions for bath that I've seen before include "Stopper for hole (don't let 8 through it!)" , "Somerset spa" , "Hot tub" , "Check of books" , "Historic spa town" .)