So, you have a very tight chamber. Not to SAAMI spec. Two things can go wrong. The dangerous one first:
Some tight custom chambers have chamber necks that are below standard size and you are supposed to outside-turn the necks to fit in. They will not load and shoot factory ammo safely. If you have this you MUST outside turn necks to the custom spec or you can have a failure to properly release the bullet and can have very high overpressure. Usually, a custom smith will stamp the loaded round outside neck OD on the barrel somewhere. Cases must be turned down so the neck walls are not thick enough to exceed that dimension with a bullet inserted into them.
If that is not the case and the rest of the case is what is not fitting, you may need a small base die. Having a die custom made is possible. The standard industry tolerance is ±0.002", which isn't all that tight, so some dies may work when others in the same brand do not. Call Lee or Redding or Forster and find out what they need to get you a working die. Usually, they can tell from fired cases you send them, but do check the neck thing I mentioned above, first, before shooting anything it the rifle.