Employ an American egghead (3)
I believe the answer is:
use
'employ' is the definition.
('use' can be a synonym of 'employ')
'an american egghead' is the wordplay.
'an american' becomes 'us'.
'egghead' becomes 'e' (head letter of 'egg').
'us'+'e'='USE'
(Other definitions for use that I've seen before include "Apply, employ" , "Habitually employ" , "Profit" , "Take drugs regularly" , "Custom - service" .)