Offer to look after Her Majesty (6)
I believe the answer is:
tender
'offer' is the definition.
(tender offer is a kind of offer)
'look after her majesty' is the wordplay.
'look after' becomes 'tend' (tending is a kind of looking after).
'her majesty' becomes 'er' (Elizabeth Regina).
'tend'+'er'='TENDER'
'to' is the link.
(Other definitions for tender that I've seen before include "Bill from Avon's beloved" , "Ship that provides supplies to other ships" , ". . . . . . is the Night (F. Scott Fitzgerald)" , "Gentle, fond (6)" , "Offer; sore" .)