Half of sect involved in secret compact (5-3)

I believe the answer is:

close-set

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'compact' is the definition.
Both the answer and definition are adjectives. Maybe they are linked in a way I don't understand?

'half of sect involved in secret' is the wordplay.
'half of' indicates taking half.
'involved in' means one lot of letters goes inside another.
'secret' becomes 'closet' (synonyms).
'sect' cut in half is 'se'.
'se' placed into 'closet' is 'CLOSE-SET'.

Can you help me to learn more?

(Other definitions for close-set that I've seen before include "(Eg of eyes) very near to each other" , "Tight together" , "With little space between them, eyes perhaps" .)

I've seen this clue in The Hindu.

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