A soldier gets embroiled in trouble - slowly (6)

I believe the answer is:

adagio

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'slowly' is the definition.
(musical term)

'a soldier gets embroiled in trouble' is the wordplay.
'soldier' becomes 'GI' (term for US soldier).
'gets' is an insertion indicator.
'embroiled in trouble' becomes 'dao' (I am not sure about this - if you are sure you should believe this answer much more).
'gi' placed within 'dao' is 'dagio'.
'a'+'dagio'='ADAGIO'

Can you help me to learn more?

(Other definitions for adagio that I've seen before include "In music, leisurely" , "'Slowly and gracefully, in music (6)'" , "In slow tempo" , "moving slowly" , "Slow movement (music)" .)

I've seen this clue in The Irish Times.

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