UK is supporting British drink — they have strings attached (9)

I believe the answer is:

bouzoukis

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'they have strings attached' is the definition.
I know nothing about this answer so I cannot judge whether this works.

'uk is supporting british drink' is the wordplay.
'supporting' means one lot of letters go next to another (in a down clue, some letters go below others).
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'drink' becomes 'ouzo' (ouzo is a kind of drink).
'uk'+'is'='ukis'
'b'+'ouzo'='bouzo'
'ukis' put after 'bouzo' is 'BOUZOUKIS'.

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I've seen this clue in The Guardian.

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