Message European man picked up (5)
I believe the answer is:
'message' is the definition.
(email is a type of message)
'european man picked up' is the wordplay.
'european' becomes 'E' (abbreviation e.g. EU).
'man' becomes 'liam' (man's name).
'picked up' is a reversal indicator.
'liam' backwards is 'mail'.
'e'+'mail'='EMAIL'
(Other definitions for email that I've seen before include "Messages via the internet" , "Messages between computer terminals" , "Digital message" , "Electronic communication" , "Electronic message" .)