Club let another prince enjoy an all in fight (6,5)

I believe the answer is:

battle royal

I'm a little stuck... Click here to teach me more about this clue!

'fight' is the definition.
(I've seen this before)

'club let another prince' is the wordplay.
'club' becomes 'bat' (as in sporting equipment).
'another' is an anagram indicator.
'prince' becomes 'royal' (prince is a type of royal).
'let' with letters rearranged gives 'tle'.
'bat'+'tle'+'royal'='BATTLE ROYAL'

'enjoy an all in' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for battle royal that I've seen before include "Fiercely-contested fight" , "Fiercely contested dispute" , "Fiercely contested fight" , "Fierce fight" , "long row" .)

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

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