Tender chicken for example, not rook (3)
I believe the answer is:
bid
'tender' is the definition.
(synonyms)
'chicken for example not rook' is the wordplay.
'chicken for example' becomes 'bird' (chicken is a kind of bird).
'not' indicates named letters should be taken away.
'rook' becomes 'R' (chess abbreviation).
'bird' with 'r' removed is 'BID'.
(Other definitions for bid that I've seen before include "Offer a price" , "Make an offer at auction" , "Offer (for); demand" , "Try" , "Propose a payment" .)