Minister to finish after a heartless taunt (6)
I believe the answer is:
attend
'minister to' is the definition.
(thesaurus)
'finish after a heartless taunt' is the wordplay.
'finish' becomes 'end' ('end' can be a synonym of 'finish'**).
'after' is a charade indicator (letters next to each other).
'heartless' says to hollow out the word (remove centre letters).
'taunt' with its middle taken out is 'tt'.
'a'+'tt'='att'
'end' put after 'att' is 'ATTEND'.
(Other definitions for attend that I've seen before include "minister" , "put in an appearance" , "Be present at, or accompany" , "Be there ? pay attention" , "notice" .)