Notice a soldier with love for slow music (6)

I believe the answer is:

adagio

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'slow music' is the definition.
'adagio' can be an answer for 'music' (adagio is a kind of music). I am not sure about the 'slow' bit.

'notice a soldier with love' is the wordplay.
'notice' becomes 'ad'.
'soldier' becomes 'gi' (government issue or general issue).
'with' says to put letters next to each other.
'love' becomes 'o' (In tennis, 'love' means 'zero').
'ad'+'a'+'gi'+'o'='ADAGIO'

'for' is the link.

Can you help me to learn more?

(Other definitions for adagio that I've seen before include "In slow tempo" , "going slowly in work" , "Slow movement (music)" , "In slow time (music)" , "Musical composition to be played slowly and gracefully" .)

I've seen this clue in The Telegraph.

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