This is an interesting question...
As far as I remember there is no canon information on the subject, other than possibly when Hyzenthlay became co-Chief in TFWD. If I remember correctly, Hazel suggested it, Hyz approved, and nobody objected, so it happened.
But after Hazel's death, I don't know what would happen...maybe he would choose a successor some time before?
Other warrens might have other ways of doing things, though.