Crossword Genius

Landlord initially thrown by elusive girl’s rental arrangement (10)

Ross

I believe the answer is:

subtenancy

I'm a little stuck... Click here to teach me more about this clue!

'landlord initially thrown' is the definition.
I can't tell whether this defines the answer.

'elusive girl's rental arrangement' is the wordplay.
'elusive girl' becomes 'sub' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'rental arrangement' becomes 'tenancy' (I've seen this before).
'sub'+'tenancy'='SUBTENANCY'

'by' is the link.

Can you help me to learn more?

I've seen this clue in The Times.
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