Give more than generous cover (7)
I believe the answer is:
smother
'generous cover' is the definition.
'smother' can be an answer for 'cover' (thesaurus). I am not certain of the 'generous' bit.
'give more' is the wordplay.
'give' becomes 'sm' (I can't justify this - if you can you should give a lot more credence to this answer).
'more' becomes 'other' (synonyms).
'sm'+'other'='SMOTHER'
'than' is the link.
Can you help me to learn more?
(Other definitions for smother that I've seen before include "don't give enough freedom" , "2 (anag)" , "Prevent from breathing" , "Put out" , "Kill by depriving of air" .)