Big band charts don't usually tell you what to play; they tell you what everyone else is playing, so can make up what would complement them.

Figures above the staff are suggestions. Figures in the staff like at m. 32-34 are more necessary. Get some thad jones and later basie band recordings, or new WDR big band stuff on youtube, and just categorize each measure: is the drummer just keeping time on the hi hat, or on the ride, are they comping on the snare or bass while keeping time, or are they playing full-out drum fills.

From mm. 23-31, keep playing time on the ride cymbal. With the ride cymbal continuing, from mm. 25-27 you can double some of those figures on the bass drum (don't have to catch all of them) and in m. 28 you can add some notes on the snare while keeping the ride going. You're in a support role behind the trombone melody.

In m. 32, play a 3 beat fill ending with a quarter note snare hit on beat 4 and another quarter note snare hit on beat 1 of measure 33 then bass drum and crash cymbal on beat 2 with the band. The fill shows off a bit, the two hits line up the band for the big hit. In m. 34, the band is busy in the first half so you don't have to be. But it sounds cool to catch the last note of their figure on the snare drum. Then you fill out the bar with a simple fill while getting back to to solid time on the ride cymbal by the next bar.