Old private detective consumed narcotic (6)
I believe the answer is:
opiate
'narcotic' is the definition.
(opiate is a kind of narcotic)
'old private detective consumed' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'private detective' becomes 'pi' ('PI' can be a synonym of 'private detective').
'consumed' becomes 'ate' (eating is a kind of consuming).
'o'+'pi'+'ate'='OPIATE'
(Other definitions for opiate that I've seen before include "Drug with an opium base" , "dope" , "It induces sleep" , "Type of drug" , "Sedating drug" .)