In archaeological operation everyone favoured old-style communication process (8)
I believe the answer is:
dialling
'old-style communication process' is the definition.
(dialling a phone)
'in archaeological operation everyone favoured' is the wordplay.
'in' indicates putting letters inside.
'archaeological operation' becomes 'dig' (archaeological dig or excavation).
'everyone' becomes 'all' (all people).
'favoured' becomes 'in' (I've seen this in other clues).
'all'+'in'='allin'
'dig' going around 'allin' is 'DIALLING'.
(Other definitions for dialling that I've seen before include "given a certain tone" , "starting the call" .)