Accessory in Tamworth criminal group on edge (4-4)

I believe the answer is:

nose-ring

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'accessory in tamworth' is the definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Perhaps you can see an association between them that I don't see?

'criminal group on edge' is the wordplay.
'criminal group' becomes 'ring' (ring can mean a group of criminals).
'on' means one lot of letters go next to another.
'edge' becomes 'nose' (I can't justify this - if you can you should give a lot more credence to this answer).
'ring' after 'nose' is 'NOSE-RING'.

Can you help me to learn more?

I've seen this clue in The Times.

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