Bury — popular market, quite popular ultimately (5)
I believe the answer is:
inter
'bury' is the definition.
(to inter is to put into the ground)
'popular market quite popular ultimately' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'ultimately' suggests the final letters.
The last letters of 'market quite popular' are 'ter'.
'in'+'ter'='INTER'
(Other definitions for inter that I've seen before include "top Italian side" , "Set deep" , "Place in ground" , "Bury (or, perhaps, Milan)" , "Place into grave, tomb" .)