Does nothing get Satan annoyed with saint? (9)

I believe the answer is:

stagnates

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'does nothing get satan annoyed with saint?' is the definition.
I can't tell whether this definition defines the answer.

'get satan annoyed with saint?' is the wordplay.
'annoyed with' indicates anagramming the letters.
'saint?' becomes 's'.
'get'+'satan'='getsatan'
'getsatan' with its letters mixed up with 's' makes 'STAGNATES'.

Can you help me to learn more?

(Other definitions for stagnates that I've seen before include "Festers" , "doesn't develop" , "becomes inactive" .)

I've seen this clue in The Times and The Sunday Times.

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