At a minimum, pull the fuel tank drain plug and drain the old gas. I would also disconnect the fuel line at the tank side of the fuel pump and blow the tank line clear with air-with gas cap off. Also a good idea to clean out the fuel filter or replace if disposable type. It should have a glass bowl style filter but after 52 years, you could find just about anything.
Depending on how long it's been sitting, you may have to rebuild the carb but maybe you should try it first. Put a bottle of fuel injector cleaner in the first tank of fresh gas.
Not fuel related, but when something has been unused for an extended period, you can get rust/pitting in whichever cylinder the intake valve is open on. Always a good practice to pull all the plugs and squirt some lube in the cylinders and then crank it over with the plugs out. I usually give it a good shot of PB Blaster followed by about a 1/4 cup of Marvel Mystery Oil. Crank it long enough to blow most of that out-still without plugs. All that stuff will make a cloud when you do get it started but may add quite a few miles before a rebuild.
If it was mine, the oil and coolant would also be changed out before trying to start it. If the present oil smells like old gas, it is also probable that the fuel pump diaphragm is shot and leaking gas into the oil.
If this isn't your first old Jeep, you may know about the parts issues. If it is, I would recommend parts from Walack's and Peter Debella. Stay away from anything Omix-Ada and Crown if at all possible. While there is some usable stuff coming from those people, most of it is junk. If you order from places like Kaiser Willys and Willys Overland ask them about the suppliers of the pieces you are ordering. Debella has a lot of NOS parts and those are definitly worth the money.
1947 CJ 2A, 1949 CJ 3A, 1955 CJ 3B, 1968 CJ 5, 2012 JKUR