Beg for quarter in the wood (7)
I believe the answer is:
beseech
'beg' is the definition.
(I've seen this before)
'quarter in the wood' is the wordplay.
'quarter' becomes 'se'.
'in the' indicates putting letters inside.
'wood' becomes 'beech' (beech is a kind of wood**).
'se' going into 'beech' is 'BESEECH'.
'for' acts as a link.
(Other definitions for beseech that I've seen before include "Entreat, implore" , "wood" , "pray" , "Sue" , "Fervently ask (someone) for something" .)