Having met me leaving, enquire after a job (4)
I believe the answer is:
task
'a job' is the definition.
('task' can be a synonym of 'job')
'having met me leaving enquire' is the wordplay.
I cannot quite understand how this works, but
'enquire' could be 'ask' (to enquire is to ask or question) and 'ask' is found within the answer.
A single letter 't' remains which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
'after' is the link.
Can you help me to learn more?
(Other definitions for task that I've seen before include "Burden with work" , "Allocate work" , "Job to be done" , "Set piece of work" , "Job, undertaking" .)