Crossword Genius

Composer found at seaside, having left the East (4)

Ross

I believe the answer is:

bach

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'composer' is the definition.
(Johann Sebastian Bach)

'seaside having left the east' is the wordplay.
'seaside' becomes 'beach' (a beach is found by the seaside).
'having left' indicates named letters should be taken away.
'the east' becomes 'E' (abbreviation).
'beach' with 'e' taken out is 'BACH'.

'found at' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for bach that I've seen before include "Musical family" , "German composer (affectionate to a Welshman?)" , "Family of German composers" , "musical great" , "Johann Sebastian . . . . , great composer (4)" .)

I've seen this clue in The Irish Times.
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