A bird's exciting times out (8)

I believe the answer is:

titmouse

'a bird's' is the definition.
(titmouse is a kind of bird)

'exciting times out' is the wordplay.
'exciting' indicates anagramming the letters.
'times'+'out'='timesout'
'timesout' with letters rearranged gives 'TITMOUSE'.

(Other definitions for titmouse that I've seen before include "Small bird" , "Small songbird" .)

I've seen this clue in The Telegraph.

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