Quietly mention favour (6)
I believe the answer is:
prefer
'favour' is the definition.
(synonyms)
'quietly mention' is the wordplay.
I cannot quite see how this works, but
'quietly' could be 'p' (p for piano and quiet) and 'p' is found within the answer.
The remaining letters 'refer' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for prefer that I've seen before include "Tend to choose (one thing over another)" , "Like (something) better than another" , "Favour, like better" , "Advance" , "support" .)