As a minimum. in addition to trailer tires, check the trailer brakes to be sure they still work as designed. If the brakes don't work then I would probably just replace the axle assemblies with new axles, including electric brakes. Dexter axle probably makes the axles that will fit your trailer, but you must measure the length of the axle to be sure you replace them with the correct length of axles.
If the brakes work fine, then I would remove the wheels and hubs and repack the wheel bearings by hand. Be sure and use only very high quality wheel bearing grease, not ordinary grease gun grease. You can use a bearing packer gizmo, but do not rely on simply using a grease gun. Here's my wheel bearing hand packer gizmo:
Most auto parts stores should have at least one version of a wheel bearing packer in stock if you don't want to order over the internet.
You won't need a gizmo like that one if you know how to use just your hands to get all the old grease out of the inside of the bearings and replace it with new high-quality wheel bearing grease. But we're talking about getting ALL
the old grease out of the bearings. On a 40-year old trailer, that may be impossible to accomplish, so you may need to replace the bearings with new ones, then hand-pack the new bearings. Take the old bearings to an auto parts store and they should be able to match the old bearings with new ones.
With new tires pumped up to the max PSI on the sidewall, good trailer brakes and good wheel bearings hand packed with new high-quality wheel bearing grease, you should be ready to go.
Then after you get it home, you'll be ready for the joys of maintaining a 40-year old TT. You may need to replace or overhaul the AC, hot water heater, water pump, cooktop and oven, holding tank(s), water and gas lines, propane tanks, power supply control box. etc., etc.