Bears snare bag-carrier (8,5)

I believe the answer is:

shoulder strap

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'bears snare' is the definition.
The answer and definition can be both man-made objects as well as being singular nouns.
Perhaps there's an association between them I don't understand?

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for shoulder strap that I've seen before include "One supporting slip" , "A supporter" .)

I've seen this clue in the Sydney Morning Herald.

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