Jeep AWD

Will 1 mismatched new tire cause seal bearing to go out prematurely in jeep awd 2003 grand cherokee?

It could. When you have different diameters of tires on a 4wd vehicle, you’re forcing the differential to operate full-time, which builds up heat inside and can do all sorts of damage. You should always have equal-diameter tires on all 4 wheels, which means either replacing all 4 tires at once, or having the new tire’s tread shaved down to match the other tires (if, that is, you can find a place willing to do this)