What makes a good replacement singer In a rock band tomorrow?

Basically...

1) Can they sing

2) How well they know the songs

Lots of "classic rock" bands still touring have lost their lead singers to ill health, death, or unrecoverable disagreement. The first requirement is that the replacement be able to reproduce the sound for which the band is known, which usually means good vocal imitation rather than bringing their own spin and style. Lots and lots of bands do this just fine: Kansas, Yes, Black Sabbath, Styx...

FWIW, the bands find their new singers from tribute bands fairly often. These guys already sound right and know the material.

Second is that they fit in with the band in terms of appearance and showmanship. The band Journey hired a young man who sounds great but does not fit the band's persona at all. He's flashy in appearance where they're laid back, and he leaps around while they're subdued.