Conclusion's heartless language (6)
I believe the answer is:
finish
'conclusion's' is the definition.
(synonyms)
'heartless language' is the wordplay.
'heartless' says to hollow out the word (remove centre letters).
'language' becomes 'Finnish' (language of Finland).
'finnish' with its centre removed is 'FINISH'.
(Other definitions for finish that I've seen before include "completion" , "train socially" , "Complete (6,3) - See 16" , "Conclude, stop" , "Put the final touches to" .)