What do we call the person who leads an orchestra this way?

A conductor is the person who leads an orchestra, standing at the front and waving a small stick called a baton to show the musicians when to start, stop, play louder or softer, and stay together in time. Without someone keeping everyone lined up, dozens of musicians playing different instruments could easily drift out of sync.

A composer is the person who writes the music before it's ever performed, and a singer is just one type of performer among many, so neither role matches someone standing in front waving a baton to guide a whole group.

Conductors often memorize entire lengthy pieces of music so they can watch the musicians instead of staring down at sheet music the whole time.