Having met me leaving, enquire after a job (4)
I believe the answer is:
task
'a job' is the definition.
(synonyms)
'having met me leaving enquire' is the wordplay.
I cannot really understand how this works, but
'enquire' could be 'ask' (to enquire is to ask or question) and 'ask' is located in the answer.
A single letter 't' remains which might be clued in a way I don't understand.
This explanation may well be incorrect...
'after' acts as a 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" .)