Wearing kit, Italian club set to play Partisan side (6,8)

I believe the answer is:

vested interest

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'partisan side' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.

'wearing kit italian club set to play' is the wordplay.
'wearing kit' becomes 'vested' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'italian club' becomes 'inter' (Inter Milan football club).
'to play' indicates an anagram.
'set' with letters rearranged gives 'est'.
'vested'+'inter'+'est'='VESTED INTEREST'

Can you help me to learn more?

(Other definitions for vested interest that I've seen before include "Having personal concern" , "Personal stake in an undertaking" , "It could be good for you!" .)

I've seen this clue in The Times.

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