Yank in London’s Burning (4)

I believe the answer is:

itch

'burning' is the definition.
(both can mean a strong desire)

I don't understand how the rest of the clue works.

(Other definitions for itch that I've seen before include "Contagious skin infection" , "Prickling" , "Hunger, longing" , "following seven years in union?" , "Nagging wish" .)

I've seen this clue in The Times.

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