Killer's hot Italian mother beginning to network (6)
I believe the answer is:
hitman
'killer's' is the definition.
(I've seen this before)
'hot italian mother beginning to network' is the wordplay.
'hot' becomes 'h' (abbreviation eg on taps).
'italian' becomes 'it' (abbreviation for Italian).
'mother' becomes 'ma' (Ma is another word for mother or mum).
'beginning to' says to take the initial letters.
The first letter of 'network' is 'n'.
'h'+'it'+'ma'+'n'='HITMAN'
(Other definitions for hitman that I've seen before include "killer" , "Hired gun" , "offer?" , "Assassin" .)