You'll probably have to buy a new reverse lever. The lever has the splines machined on the inside of the hole in the lever. There are matching splines on the reverse shaft that the lever goes on. The splines are the little grooves or notches that keeps the lever from slipping on the reverse shaft.
If the splines on the reverse shaft are worn off, then you will have to have a new reverse shaft also. Hopefully, the splines won't be worn all the way down and you can get by with just buying the reverse lever.