Dishonest person has left with air-conditioning (4)
I believe the answer is:
liar
'dishonest person' is the definition.
(I've seen this in another clue)
'left with air-conditioning' is the wordplay.
I cannot quite see how this works, but
'left' could be 'l' (common abbreviation) and 'l' is present in the answer.
an anagram of 'air' is 'iar' which is within the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
'has' is the link.
Can you help me to learn more?
(Other definitions for liar that I've seen before include "Dissembler" , "Phoney" , "Teller of fibs" , "Rail at a prevaricator" , "Bearer of false witness" .)