Principal town of the Isle of Bute (8)

I believe the answer is:

rothesay

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'principal town' is the definition.
'rothesay' can be an answer for 'town' (I have seen 'Scottish town' mean 'rothesay' so perhaps 'town' could also mean 'rothesay'). I am not certain of the 'principal' bit.

I can't explain the rest of the clue.

Can you help me to learn more?

(Other definitions for rothesay that I've seen before include "Scottish town" , "Town on Isle of Bute" , "Chief town on Bute; so hearty (anag.)" , "Main town on Bute" .)

I've seen this clue in The Times.

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