Little devil learning to beg (7)
I believe the answer is:
implore
'to beg' is the definition.
(synonyms)
'little devil learning' is the wordplay.
'little devil' becomes 'imp' (an imp is a little demon).
'learning' becomes 'lore' (both can mean tradition or knowledge).
'imp'+'lore'='IMPLORE'
(Other definitions for implore that I've seen before include "More lip (anag)" , "Beg earnestly, beseech" , "Beg earnestly, entreat" , "Beg earnestly, plead" , "Ask earnestly" .)