Half-heartedly mouth entertaining answer for emperor (6)
I believe the answer is:
kaiser
'emperor' is the definition.
(German term for emperor)
'half-heartedly mouth entertaining answer' is the wordplay.
I cannot really see how this works, but
'heartedly' could be 'er' (I've seen this in other clues) and 'er' is present in the answer.
'answer' could be 'a' (abbreviation eg in Q and A) and 'a' is located in the answer.
This explanation may well be incorrect...
'for' is the link.
(Other definitions for kaiser that I've seen before include "Former German emperor" , "Old German emperor like Bill" , "Old German emperor, pre-Hitler" , "Ruler over empire" , "Austrian bigwig" .)