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