Naughty child trapping worn out animal (5,3)

I believe the answer is:

brown rat

'animal' is the definition.
The answer is an example.

'naughty child trapping worn out' is the wordplay.
'naughty child' becomes 'brat'.
'trapping' means one lot of letters goes inside another.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'worn' with letters rearranged gives 'ownr'.
'brat' going around 'ownr' is 'BROWN RAT'.

(Another definition for brown rat that I've seen is " Common rodent pest".)

I've seen this clue in The Guardian.

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