cut in
• (of a motor or other mechanical device) begin operating, especially when triggered automatically by an electrical signal.
• "seconds later the emergency generators cut in"
• interrupt someone while they are speaking.
• "‘It's urgent,’ Raoul cut in"
• pull in too closely in front of another vehicle after having overtaken it.
• "the bus driver, seeing that the car on the outside was cutting in, should have braked gently and avoided any collision"
• include someone in a deal and give them a share of the profits.
• "it annoyed the hell out of him that she hadn't cut him in"
• interrupt a dancing couple to take over from one partner.
• "Saturday night she goes to an informal dance where men are rare and any girl may cut in"
cut-in
noun
• a shot in a film that is edited into another shot or scene.
• "the frequent cut-ins to people skiing over cliffs had less relevance"