AFL's pact inexplicably lets pets enter (8)

I believe the answer is:

catflaps

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'pets enter' is the definition.
I don't know anything about this answer so I can't judge whether this works.

'afl's pact inexplicably' is the wordplay.
'afl's pact' can be anagrammed to 'CATFLAPS'.
But, I am not clear how the anagram is indicated.

'lets' is the link.

Can you help me to learn more?

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

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