I have a little experience doing this. Did it at a go-kart track and it worked until the owner got stupid. Tried it at a car track but couldn't get the support that racers promised.
First you've got to meet with drivers / car owners / teams to see if there is anybody truly interested. One-on-one talks are okay, but if you decide to go forward it helps to have a big meeting to hash out rules etc. It can help to borrow rules from similar existing classes in other areas.
Second you need to talk to local car builders to find out what your proposed car would really cost - both to build and also to maintain. Then compare that to the costs for comparable classes. Also compare it to classes that are declining because you might want to lure those teams to your new class. If the new class can use any parts from a declining class you might get teams to switch. Another consideration is if there are existing classes in your area that already use some of the parts your new class would use, such as motors. Particularly if you notice that those teams don't have an affordable path to step up from what they're running to a higher class (such as from modified engine stock bodied 4-cyclinder cars to Late Models). You might be able to position your new class as a step up that can incur lessor switching costs. For example, stock bodied 4-cyclinder to your new 4-cylinder modifieds to 8-cylinder modifieds.
Third, if you think you have enough interest from local teams and the costs appear affordable, you'll need to go out on a limb and schedule the class. Expect to suffer low car counts and low revenues from it at first, but you need to show you're committed before some of the teams will join. It can be expensive for teams to change classes so they may wait and see if you'll keep the class before they spend the money on it. Sponsors can act the same way.
Some experiences from trying this kind of thing before:
You'll get a lot more verbal support at first than actual car count support. If you soldier on for at least two seasons you should win teams over, provided your formula is cost -effective.
That kart track owner that got stupid killed our new class by allowing exceptions to the rules that gave new cars unfair advantages and obsoleted the existing cars overnight. Create rules and stick with them. It's okay to tweak rules for unexpected problems, but you can't obsolete major components overnight and you've got to keep your cost target always in sight.
Determine your new class rule package as soon as possible - before this season is over. The longer you wait to release tech specifications the less time teams will have to build your cars, and the less likely they will build them.
You can build good will with your new class teams by hosting free or low cost practice sessions at the track(s) that will run the class. Teams will want to test and tune their new cars.
The car track that couldn't get support has a reputation for making sudden radical rules changes, and doing it often. Racers have been stung by building for a promised set of rules, only to either face expensive changes soon into the season or find the track gave up on the class after only a couple of months. Now those racers are skeptical whenever that track announces new classes or even rules changes for existing classes, and its car count is suffering accordingly. That's why I say you'll have to soldier on with the class even though you could lose money on it at first. At the kart track we got excellent racer support after about half a season, but part of why was we hit upon a cheap set of equipment that lots of people already had sitting around. Your new 4-cylinder modified class may not have such a built-in equipment base, but if your projected costs are favorable against other classes you may still get plenty of converts.
Best of luck!