Ask earnestly for fairy stories? (7)
I believe the answer is:
implore
'ask earnestly' is the definition.
(I've seen this before)
'fairy stories?' is the wordplay.
'fairy' becomes 'imp' (imp is a kind of fairy).
'stories?' becomes 'lore' (lore can mean a body of traditions or learning).
'imp'+'lore'='IMPLORE'
'for' acts as a link.
(Other definitions for implore that I've seen before include "Beg earnestly, plead" , "Beg desperately" , "Beg earnestly, entreat" , "Beg earnestly, beseech" , "More lip (anag)" .)