Pests lead battle over right to possess celeb's mirror (5,4)

I believe the answer is:

brown rats

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'pests' is the definition.
Although both the answer and definition are plural nouns, I don't understand how they can define each other.

'lead battle over right to possess celeb's mirror' is the wordplay.
'lead' suggests taking the first letters (I've seen 'leading' mean this).
'over right' becomes 'r' (common abbreviation. I am not sure about the 'over' bit.).
'to possess' becomes 'own' ('own' can be a synonym of 'possess').
'celeb' becomes 'star' (I've seen this before).
'mirror' is a reversal indicator (I've seen 'mirrored' mean this).
The first letter of 'battle' is 'b'.
'star' backwards is 'rats'.
'b'+'r'+'own'+'rats'='BROWN RATS'

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.

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