
By "stub axle" JimD means one-wheel-drive, not a two-wheel drive "live axle" setup.
The original Brister's name is long out of business and defunct. They were absorbed by Manco/American Sportworks, so you won't find parts readily available for them. But that doesn't matter since yours is a fun kart and they use generic off-the-shelf parts mostly.
Yours looks mildly modified. It appears it was originally a two-seater (it has a wide bench style seat instead of single bucket) that was converted to single rider by moving the steering wheel to the right/center and moving the gas pedal over. I could be mistaken though.
Here's some Brister's info on another forum (posts #4 and #10 specifically):
https://www.oldminibikes.com/forum/index.php?threads/just-got-it-tonight-what-is-it.122560/
1. I'd get matching tires for the rear (or all four corners, and matching rims might be better( all one size for commonality among parts). Just my opinion and not completely necessary
2. Looks like you need a throttle cable (unless you already have one) and hardware to connect the brake rod to the pedal
3. I'm guessing #35 chain for the sprocket (count the teeth on the wheel sprocket to be sure, we'll use that info to get the right gear ratio)
4. A basic centrifugal clutch
5. More horsepower! I'd have to recommend a 6.5 HP Predator 212cc (or clone engine of your choice) to get the little beasty running
6. ?