Offer to take care of the Queen (6)
I believe the answer is:
tender
'offer' is the definition.
(tender offer is a kind of offer)
'take care of the queen' is the wordplay.
'take care of' becomes 'tend' (tending is a kind of taking care of).
'the queen' becomes 'er' (Elizabeth Regina).
'tend'+'er'='TENDER'
'to' is the link.
(Other definitions for tender that I've seen before include "Offer for acceptance" , "easily crushed" , "Bid; kindly" , "Offer - present - gentle - nurse" , "Make bid as for contract" .)