Crossword Genius

Send carriage that's turned up for one not fully engaged (4-5)

Ross

I believe the answer is:

part-timer

I'm a little stuck... Click here to teach me more about this clue!

'send carriage that's turned up' is the definition.
I can't tell whether this defines the answer.

'one not fully engaged' is the wordplay.
I cannot quite understand how this works, but
'one' could be 'me' (a setter might use 'one' to humourously mean 'me') and 'me' is present in the answer.
This explanation may well be incorrect...

'for' is the link.

Can you help me to learn more?

(Other definitions for part-timer that I've seen before include "One working reduced hours" , "One working less than a full week" , "One not working the whole week" , "Casual worker" , "worker on reduced hours" .)

I've seen this clue in The Guardian.
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