Its more out of tune, but give undue praise (7)
I believe the answer is:
flatter
'praise' is the definition.
(I know that flatter is a type of praise)
'its more out of tune but give undue' is the wordplay.
I cannot really understand how this works, but
'out of tune' could be 'flat' (I've seen this in another clue) and 'flat' is found in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for flatter that I've seen before include "Become" , "Praise obsequiously" , "drier" , "Over-praise" , "Possibly imitate" .)