Kitty admits problem — small talk (4-4)

I believe the answer is:

chit-chat

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'small talk' is the definition.
'chit-chat' can be an answer for 'talk' (I have seen 'Inconsequential talk' mean 'chit-chat' so perhaps 'talk' could also mean 'chit-chat'). I am unsure of the 'small' bit.

'kitty admits problem' is the wordplay.
'kitty' becomes 'cat'.
'admits' means one lot of letters goes inside another (to admit is to allow in).
'problem' becomes 'hitch' (hitch can mean a problem or delay).
'cat' enclosing 'hitch' is 'CHIT-CHAT'.

Can you help me to learn more?

(Other definitions for chit-chat that I've seen before include "Inconsequential talk" , "Idle nattering" .)

I've seen this clue in The Times.

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