Old American found in middle of piazza by investigator (5)
I believe the answer is:
aztec
'old american' is the definition.
(I've seen this before)
'middle of piazza by investigator' is the wordplay.
'middle of' indicates the central letters.
'by' is a charade indicator (letters next to each other).
'investigator' becomes 'tec' (short for 'detective').
The centre of 'piazza' is 'az'.
'az'+'tec'='AZTEC'
'found in' is the link.
(Other definitions for aztec that I've seen before include "One of Montezuma's people" , "certain old people" , "Relating to old civilisation in Mexico" , "Old Mexican Indian" , "Irish lower house" .)