Toy dog, perhaps, that's hanging loose? (6)

I believe the answer is:

lappet

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'hanging loose?' is the definition.
'lappet' can be an answer for 'hanging' (thesaurus). I am not certain of the 'loose?' bit.

'toy dog perhaps' is the wordplay.
'toy' becomes 'lap' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'dog perhaps' becomes 'pet'.
'lap'+'pet'='LAPPET'

'that's' acts as a link.

Can you help me to learn more?

(Another definition for lappet that I've seen is " Small hanging flap".)

I've seen this clue in The Telegraph.

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