It's not necessary to have a law license to serve as a Supreme Court Justice.
However, as I recall, the plea agreement that Clinton signed with the special prosecutor forbade him from practicing before the Supreme Court (the special prosecutor didn't and couldn't disbar him, that was up to the Arkansas Bar).
If one is forbidden to practice before the Supreme Court, it would be a little awkward to rationalize appointing him to its bench.
Not that a little thing like that ever kept the Clintons from doing anything...