Weary and fed up, being dismissed? (5,3)

I believe the answer is:

tired out

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'weary' is the definition.
The answer and definition are not the same part of speech. However, past participle verbs and adjectives occasionally mean the same thing.

'fed up being dismissed?' is the wordplay.
'fed up' becomes 'tired' ().
'being dismissed?' becomes 'out' (in cricket, to be out is to be dismissed).
'tired'+'out'='TIRED OUT'

'and' is the link.

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(Another definition for tired out that I've seen is " knackered".)

I've seen this clue in the Evening Standard.

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