Leaving queen a bid (5)
I believe the answer is:
offer
'a bid' is the definition.
(I know that bid can be written as offer)
'leaving queen' is the wordplay.
'leaving' becomes 'off' (as in 'I'm off').
'queen' becomes 'ER' (abbreviation for Elizabeth Regina).
'off'+'er'='OFFER'
(Other definitions for offer that I've seen before include "Present to or make a bid" , "Put forward" , "hand" , "Suggest" , "Tender or propose" .)