Musical politician in Latin home, mostly rebuilt (8)

I believe the answer is:

hamilton

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'musical' is the definition.

'latin home mostly rebuilt' is the wordplay.
'mostly' means to remove the last letter (most but not all of the word).
'rebuilt' indicates anagramming the letters.
'latin'+'home'='latinhome'
'latinhome' with its final letter taken off is 'latinhom'.
'latinhom' with letters rearranged gives 'HAMILTON'.

'politician in' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.

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(Other definitions for hamilton that I've seen before include "in Scotland or Bermuda" , "Former Tory MP" , "Emma --, Nelson's lover" , "Lady mistress of Napoleon" , "4's Emma" .)

I've seen this clue in The Guardian.

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