cut-in

(film) a still picture that is introduced and that interrupts the action of a film.

(broadcasting) a local announcement inserted into a network program.

Break into a conversation.

Allow someone to have a share or profit.

Drive in front of another vehicle leaving too little space for that vehicle to maneuver comfortably.

Interrupt a dancing couple in order to take one of them as one's own partner.

Mix in with cutting motions.