The pictures below show a pinion from a longcase escape wheel. The wear is so bad it has almost reduced the width of the pinion leaves to half of their full width. Notice also that the pivot has almost worn through.
After welding, the only way to tell if enough metal has been deposited is to grind the excess down to the correct level in order to expose any remaining hollows. If any hollows remain then more metal can be welded in.
The final step is to polish the restored part. The idea of polishing is not to make it shine but to make the surface finish the same as it would have been when new. It is not acceptable to improve an antique clock either in design or surface finish.
One alternative would be to make a whole new arbor and pinion. This would involve very extensive of work, because the wheel mounting collet would have to be removed and fitted to the new arbor, or a new collet made, and then the old wheel would have to be mounted on the new arbor. It would take some care to ensure everything ended up perfectly concentric.
Another alternative would be to mount the arbor in the lathe and remove the existing worn leaves of the pinion, then make a new pinion head and bore a hole in it and mount it onto the arbor in place of the old one. This too is not so straightforward, but it is much better than the first option. As it happens, it is an option I could recommend, because it retains all of the original material except for the worn pinion leaves. However it still needs to be set up very carefully in the lathe to ensure final perfect concentricity of the new pinion head with the pivots and the wheel.