Soldiers relaxed around hotel in Harrow, say (7,6)

I believe the answer is:

private school

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'harrow say' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.

'soldiers relaxed around hotel' is the wordplay.
'soldiers' becomes 'privates' (I've seen this before).
'relaxed' becomes 'cool' (cool can mean relaxed or calm).
'around' means one lot of letters goes inside another.
'hotel' becomes 'h' (phonetic alphabet).
'cool' going around 'h' is 'chool'.
'privates'+'chool'='PRIVATE SCHOOL'

'in' is the link.

Can you help me to learn more?

I've seen this clue in The Telegraph.

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