Very unpleasant fag would, when put out (3-5)

I believe the answer is:

god-awful

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'very unpleasant' is the definition.
(I've seen this before)

'fag would when put out' is the wordplay.
'fag would' anagrams to 'GOD-AWFUL'.
But, I'm not sure how this is indicated.

Can you help me to learn more?

(Other definitions for god-awful that I've seen before include "Very unpleasant" , "Appalling" .)

I've seen this clue in The Times.

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