Admitting case of insubordination, detective has stuck around (9)
I believe the answer is:
including
'admitting' is the definition.
('include' can be a synonym of 'admit')
'case of insubordination detective has stuck around' is the wordplay.
I cannot really see how this works, but
'detective' could be 'di' (Detective Inspector abbreviation) and 'di' is found in the answer.
'stuck' could be 'clung' ('cling' can be a synonym of 'stick') and 'clung' is found within the remaining letters.
The remaining letters 'in' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for including that I've seen before include "Adding in as part of a whole" , "Containing" , "Considering as part of the whole" .)