There are several ways to attach a thru axle wheel into this truing stand.
One possibility is to buy a tool intended for converting a thru axle wheel to have an interface similar to quick release, to be used in truing stands (these adapters are not intended for use on the bike). Shimano makes two of these adapters: TL-FH12 and TL-HB16.
TL-FH12 costs around ...
Considering that the bike is more than a dozen years old and has rim-brakes, it would be a good idea to check the state of the rims. Depending on the mileage of the bike they could easily have reached the safety limit and need replacing.
So a pair of new wheels may be an option.