Spinning out a letter to the monarch (5)

I believe the answer is:

eking

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'spinning out' is the definition.
The definition suggests a verb in its base form which matches the answer.

'a letter to the monarch' is the wordplay.
'a letter' becomes 'e'.
'to the monarch' becomes 'king' (king is a kind of monarch).
'e'+'king'='EKING'

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(Other definitions for eking that I've seen before include "Making last longer by careful use" , "Managing to make (a living)" , "spinning?" , "... stretching" , "Squeezing (out)" .)

I've seen this clue in the Evening Standard.

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