Offer to pull out (6)
I believe the answer is:
extend
This could be a double definition.
'offer' is the first definition.
('extend' can be a synonym of 'offer')
'pull out' is the second definition.
'extend' can be an answer for 'pull' (thesaurus). I am not certain of the 'out' bit.
'to' is the link.
Can you help me to learn more?
(Other definitions for extend that I've seen before include "Make larger or longer" , "Reach out, say the hand of friendship" , "Provide challenge" , "Draw out" , "Straighten out" .)