Jazz band ending on Fast City (4)
I believe the answer is:
trio
'jazz band' is the definition.
(thesaurus)
'ending on fast city' is the wordplay.
'ending on' says to take the final letters.
'city' becomes 'rio' (Rio de Janeiro).
The last letter of 'fast' is 't'.
't'+'rio'='TRIO'
(Other definitions for trio that I've seen before include "Archduke, possibly" , "Beethoven's 'Archduke', for instance" , "Beethoven's 'Archduke': famous piece written for this ensemble" , "father, spirit and son" , "Chamber group" .)