Flutes surrounding 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 not sure about the 'another' bit.

'flutes surrounding' is the wordplay.
'surrounding' says the answer is hidden in the clue.
'LUTE' is hidden within 'flutes'.

Can you help me to learn more?

(Other definitions for lute that I've seen before include "Protective packing" , "Play instrument" , "instrument that minstrel played" , "Plucked instrument; a sealant" , "Subject to drugs" .)

I've seen this clue in The Mirror.

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