Flutes surround another instrument (4)

I believe the answer is:

lute

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'another instrument' is the definition.
'lute' can be an answer for 'instrument' (lute is a kind of instrument). I'm unsure of the 'another' bit.

'flutes surround' is the wordplay.
'surround' indicates a hidden word (I've seen 'surrounding' mean this).
'LUTE' can be found hidden inside 'flutes'.

Can you help me to learn more?

(Other definitions for lute that I've seen before include "Stringed instrument shaped like a halved egg" , "clay" , "Ancient stringed instrument" , "Old musical instrument" , "Old plucked instrument" .)

I've seen this clue in The Mirror.

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