Modern communication gives them trouble (5)
I believe the answer is:
'modern communication' is the definition.
'email' can be an answer for 'communication' (email is a kind of communication). I'm unsure of the 'modern' bit.
'them trouble' is the wordplay.
'them' becomes 'em' (abbreviation).
'trouble' becomes 'ail' (synonyms).
'em'+'ail'='EMAIL'
'gives' is the link.
Can you help me to learn more?
(Other definitions for email that I've seen before include "Message sent via computer" , "Messages via the internet" , "Electronic message" , "Send one online" , "Messages between computer terminals" .)