Yes you need a new bearing and race. The 10.25 has a longer larger pinion. They should have given you everything in the kit if you got it with build kit or master kit.
Personally now that they are making actual 10.5 gears aftermarket I am just going that route.
Another thing to consider it instead of the crush sleeve for the pinion to set proper preload etc you can swap for solid washers. I think Randy's R&P offers them. This way you can measure the old one to get you close and then use the different size washer shims to get preload to spec. Then you will never have to worry about going thru crush sleeve or having a test one etc. This is what I have planned when I do my gears soon.