Tender chicken for one, not rook (3)
I believe the answer is:
bid
'tender' is the definition.
('bid' can be a synonym of 'tender')
'chicken for one not rook' is the wordplay.
'chicken for one' becomes 'bird' (chicken is a kind of bird).
'not' indicates named letters should be taken away.
'rook' becomes 'r' (abbreviation in chess).
'bird' with 'r' taken out is 'BID'.
(Other definitions for bid that I've seen before include "Offer a price" , "Order - offer" , "Try" , "Take part in auction" , "Make an offer at auction" .)