Bachelor rushes to get straps for supporting trousers (6)

I believe the answer is:

braces

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'get straps for supporting trousers' is the definition.
I can't tell whether this definition defines the answer.

'bachelor rushes' is the wordplay.
'bachelor' becomes 'B' (abbreviation e.g. BA=Bachelor of Arts).
'rushes' becomes 'races' ('race' can be a synonym of 'rush').
'b'+'races'='BRACES'

'to' acts as a link.

Can you help me to learn more?

(Other definitions for braces that I've seen before include "Supports for teeth or trousers" , "stays" , "Supports for men's trousers" , "Trouser support" , "More than one couple" .)

I've seen this clue in The Daily Express.

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