Ancient Mexican sleuth going after a Zulu (5)
I believe the answer is:
aztec
'ancient mexican' is the definition.
(I've seen this in another clue)
'sleuth going after a zulu' is the wordplay.
'sleuth' becomes 'tec' (short for detective).
'going after' says to put letters next to each other.
'zulu' becomes 'Z' (phonetic alphabet: alpha, bravo, charlie etc.).
'a'+'z'='az'
'tec' after 'az' is 'AZTEC'.
(Other definitions for aztec that I've seen before include "Such as Moctezuma" , "Early Mexican civilisation" , "Old Mexican Indian" , "Early Mex. People" , "nickname of US State" .)