Shed one had a nap in (7,3)

I believe the answer is:

dropped off

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'had a nap in' is the definition.
The definition and answer can be both related to bodily activities as well as being past participle verbs.
Perhaps they are linked in a way I don't understand?

'shed one' is the wordplay.
'shed' becomes 'dropped' (synonyms).
'one' becomes 'off' (I can't justify this - if you can you should believe this answer much more).
'dropped'+'off'='DROPPED OFF'

Can you help me to learn more?

I've seen this clue in the Evening Standard.

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