Payment by new tenant, important — one breaks into surprised expression (3,5)

I believe the answer is:

key money

'payment by new tenant' is the definition.
(money paid by a tenant for a key)

'important one breaks into surprised expression' is the wordplay.
'important' becomes 'key' (similar in meaning).
'breaks into' indicates putting letters inside.
'surprised expression' becomes 'my' (as in 'oh my!').
'one' going inside 'my' is 'money'.
'key'+'money'='KEY MONEY'

I've seen this clue in The Times.

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