That is the major problem with clubs that death is the only way to get kicked out if the leader is a npc when he dies, the game don't consider him disqualified or dead. Also if the game does recongize that he died, but there is no way to reach another sim for leader, it is either the other sims are not reachable or they are in the middle of a age transition.
Club leaders are choosen based on relationship with leader sim. So if all club members have same relationship game can't tell who is new leader until the relationships change. Also clubs have a bad habit of not updating until they meet up. However, says the club can gather that is actually not the issue, the issue with the club is it has no leader, so to fix that. Get to know the sims that are in that club, if you want to be leader, ask club members about leader, and talk down leader, you can than take control of club.
Edit since the leaders dead you can't ask the leader to step down, you may have ask one of the current club members to be leader, than you can take over.
