Old Mexican Indian, a variable investigator (5)
I believe the answer is:
aztec
'old mexican indian' is the definition.
(I've seen this before)
'a variable investigator' is the wordplay.
'variable' becomes 'z' (algebra).
'investigator' becomes 'tec' (short for 'detective').
'a'+'z'+'tec'='AZTEC'
(Other definitions for aztec that I've seen before include "Historical S. American" , "Early Mexican civilisation" , "One of Montezuma's people" , "Pre-conquest Mexican Indian" , "Native of old Mexico" .)