Scan letters found in desk, immediately (4)

I believe the answer is:

skim

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'scan letters' is the definition.
'skim' can be an answer for 'scan' (synonyms). I am not sure about the 'letters' bit.

'in desk immediately' is the wordplay.
'in' indicates the answer is hidden within the clue.
'SKIM' is hidden within 'desk immediately'.

'found' is the link.

Can you help me to learn more?

(Other definitions for skim that I've seen before include "head" , "Remove top layer; read bits of" , "Read superficially" , "Read (something) quickly" , "Glide smoothly over" .)

I've seen this clue in The Irish Times.

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