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If it's a screech, it's the belt, take the belt off and rough pulley up, it sounds like it has got polished due to the belt slipping for a long time and will continue to slip till it has this done, could also have polished the new belt so another one may be needed!

If it's a squeek something needs lubricating!

Hard to say without hearing it, but louder in the morning usually indicates it's the belt slipping due to extra load on the alternator from starting.

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Being a classic the belt stretches over a time and sometime the alternator works loose try tightenin up cheers