Nobody in particular serving American general (3,6)
I believe the answer is:
joe public
'nobody in particular' is the definition.
(Joe Public can mean any unspecified person)
'serving american general' is the wordplay.
'serving american' becomes 'Joe' (GI Joe can mean American serviceman).
'general' becomes 'public' (I've seen this before).
'joe'+'public'='JOE PUBLIC'
(Other definitions for joe public that I've seen before include "The general populace" , "... and all those around him?" , "Man in the street" .)