Hire an egg terribly European (6)
I believe the answer is:
engage
'hire' is the definition.
(I know that employ can be written as engage)
'an egg terribly european' is the wordplay.
'terribly' indicates anagramming the letters.
'european' becomes 'E' (abbreviation e.g. EU).
'an'+'egg'='anegg'
'anegg' anagrammed gives 'engag'.
'engag'+'e'='ENGAGE'
(Other definitions for engage that I've seen before include "Hire; get to grips with" , "Become bound; attract" , "Participate" , "Take on - reserve - promise" , "Take on (eg for work, in battle)" .)