Picking up part for Chevrolet an American's issue (7)
I believe the answer is:
emanate
'issue' is the definition.
(both can mean to give out or radiate)
'picking up part for chevrolet an american's' is the wordplay.
'picking up' shows that the letters should be reversed in order (in a down clue, letters go up).
'part' says the answer is hidden in the clue.
'etaname' is hidden within 'for chevrolet an americans'.
'etaname' in reverse letter order is 'EMANATE'.
(Other definitions for emanate that I've seen before include "Flow or proceed from" , "Issue forth, from a source" , "Come forth" , "Proceed or issue forth" , "Issue or originate from manatee" .)