Person using drill interrupts speaker (8)
I believe the answer is:
operator
'person' is the definition.
(operator is a kind of person)
'drill interrupts speaker' is the wordplay.
'drill' becomes 'pe' (Physical Education).
'interrupts' is an insertion indicator.
'speaker' becomes 'orator' (orator is a kind of speaker).
'pe' inserted into 'orator' is 'OPERATOR'.
'using' is the link.
(Other definitions for operator that I've seen before include "Machinist -- or surgeon?" , "Person who directs or controls, machine say (8)." , "Driver" , "Person who runs a machine or a business" , "Mathematical symbol" .)