Fasten up sections that have turned up (5)

I believe the answer is:

strap

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'fasten' is the definition.
(I know that strap is a kind of fasten)

I don't understand the rest of the clue.

(Other definitions for strap that I've seen before include "Restraining fastener" , "Leather thong" , "Strong band for binding luggage etc" , "Narrow strip of leather" , "punishment in school" .)

I've seen this clue in The Times.

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