This clip, from the television program Jazz Party, is more than eight minutes long — but the climax is cut off. No matter, it’s great. The start is nice and informal, and the camera moves around quite a bit for a 1950s video. That adds a nice dimension. Hawkins takes his solo starting at about the 3:10 mark. The notes at YouTube identify all the players. In addition to Hawkins, they include Charlie Shavers, J.C. Higginbotham, Lester Young, Pee Wee Russell, Willie “The Lion” Smith, Sonny Greer and others.
The subject of the song — Symphony Sid — was Sid Torin (originally Tarnopol), a radio DJ who was instrumental (no pun intended) in introducing jazz to a mass audience.
Coleman Hawkins also can be seen playing tenor sax on a Stoned, apparently improvising with Charlie Parker in 1950, in a bluesy mode in South of France Blues, Centerpiece and Body and Soul. Of special note is the guitarist in the South of France Blues clip. He apparently is Mikey Baker.
Here is Coleman’s bio and a discography.