I am sorry for this delayed reply to your gardening question. We are transitioning to a new Q&A system and your question was unfortunately lost in the transition. I have discovered it now and hope this reply is not too late to be of help.
Kumquats are pretty hardy. I would cut it back to what appears to be green, undamaged wood; even if this means cutting it way back. It should be able to sprout from somewhere above the graft union near the base of the plant. Remove any sprouts emerging from below the graft union as they are rootstock sprouts which are not the same species as kumquat and thus won't bear the desired fruit.
Thanks for the question. Please stop in again soon!
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