Make use of a cigarette end after I lit up in America (7)
I believe the answer is:
utilise
'make use of' is the definition.
(synonyms)
'a cigarette end after i lit up in america' is the wordplay.
'end' suggests the final letters.
'after' means one lot of letters go next to another.
'up' is a reversal indicator (in down clue: letters go upwards).
'in' indicates putting letters inside.
'america' becomes 'us' (United States).
The final letter of 'cigarette' is 'e'.
'i'+'lit'='ilit'
'ilit' back-to-front is 'tili'.
'tili' placed into 'us' is 'utilis'.
'e' put after 'utilis' is 'UTILISE'.
(Other definitions for utilise that I've seen before include "Put into service, find application for" , "Find application or task for" , "Employ, do something with" , "Put to use" , "Employ, make use of" .)