Annoys sides playing with interrupting requests (10)

I believe the answer is:

displeases

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'annoys' is the definition.
The answer and definition can be both to do with human feelings as well as being verbs in their -s form.
Perhaps you can see an association between them that I can't see?

'sides playing with interrupting requests' is the wordplay.
'playing' is an anagram indicator.
'with' indicates putting letters inside.
'interrupting requests' becomes 'pleas' (I can't explain this - if you can you should believe this answer much more).
'sides' is an anagram of 'dises'.
'dises' going around 'pleas' is 'DISPLEASES'.

Can you help me to learn more?

(Other definitions for displeases that I've seen before include "causes irritation" , "irritates" .)

I've seen this clue in The Times.

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