segue into (something)
To transition or lead smoothly into a new state, condition, topic, section, idea, etc. The professor used the anecdote to segue into the next portion of her lecture. The scene segues into a moving musical number between the two characters.
segue into something
to make a smooth transition into something. (From filmmaking and broadcasting. Rhymes with egg - day.) At this point in the script, you should segue into the next scene. Don't segue here, this is where a commercial goes.