Start to straighten sheets for escort, as a gentleman does (6)

I believe the answer is:

squire

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'start' is the definition.
The definition and answer can be both to do with motion as well as being verbs in their base form.
Perhaps there's an association between them I don't understand?

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for squire that I've seen before include "Chief landowner of an area" , "Local landowner; knight's attendant" , "Old landowner" , "[PILGRIM in the CANTERBURY TALES]" , "Country gentleman" .)

I've seen this clue in The Guardian.

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