Complex Irishman returning service off the net? (7)

I believe the answer is:

webmail

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'service off the net?' is the definition.
I don't know anything about this answer so I cannot tell whether it can be defined by this definition.

'complex irishman returning' is the wordplay.
'complex' becomes 'web' (I can't justify this - if you can you should believe this answer much more).
'irishman' becomes 'liam' (common Irish name).
'returning' says the letters should be written backwards.
'liam' backwards is 'mail'.
'web'+'mail'='WEBMAIL'

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I've seen this clue in The Independent.

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