Speaks softly, silence getting endless praise (7)
I believe the answer is:
mumbles
'speaks softly' is the definition.
(to mumble is to speak softly)
'silence getting endless praise' is the wordplay.
'silence getting' becomes 'mum' (I can't justify this - if you can you should give a lot more credence to this answer).
'endless' means to remove the last letter.
'praise' becomes 'bless' (I've seen this before).
'bless' with its last letter taken off is 'bles'.
'mum'+'bles'='MUMBLES'
Can you help me to learn more?
(Other definitions for mumbles that I've seen before include "Speaks indistinctly" , "Swansea area" , "South Wales resort - talks indistinctly" , "Comes out with poorly" .)