Longs to have complaints abandoned by bishop (6)

I believe the answer is:

itches

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'longs' is the definition.
Although both the answer and definition are verbs in their -s form, I cannot see how they can define each other.

I can't explain the rest of the clue.

Can you help me to learn more?

(Other definitions for itches that I've seen before include "causes irritation" , "Has uncomfortable tingling sensation" , "Tingles as skin may" , "Ethics (anag)" , "They need to be scratched" .)

I've seen this clue in The Irish Times.

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