Without hesitation, king and queen hate peeled fruit (7)
I believe the answer is:
'fruit' is the definition.
(kumquat is a kind of fruit)
'without hesitation king and queen' is the wordplay.
'without' means one lot of letters goes inside another.
'hesitation' becomes 'um' (um is said in hesitation).
'king' becomes 'K' (abbreviation for king in chess).
'and' means one lot of letters go next to another.
'queen' becomes 'quat' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'um' inserted within 'kquat' is 'KUMQUAT'.
'hate peeled' is the link.
This may not be right. Some or all of it may be part of another bit of the clue.
(Other definitions for kumquat that I've seen before include "Small Chinese orange" , "Small orange fruit" , "Small oval citrus fruit" , "Chinese orange fruit" , "Asian citrus-like fruit" .)