I tug lout's pants in fight for supremacy (4,2,3)

I believe the answer is:

slug it out

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'fight for supremacy' is the definition.
'slug it out' can be an answer for 'fight' (I've seen this before). I am not sure about the 'for supremacy' bit.

'i tug lout's pants' is the wordplay.
'pants' indicates an anagram (UK informal term for 'nonsense' or 'rubbish').
'i'+'tug'+'louts'='ituglouts'
'ituglouts' anagrammed gives 'SLUG IT OUT'.

'in' acts as a link.

Can you help me to learn more?

(Another definition for slug it out that I've seen is " Fight".)

I've seen this clue in The Independent.

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