The game usually decides on a new chief when the old one dies - but if the new chief is a nursing mom, she (or her baby) won't be able to try on the robes until the baby is 2. Any other villager, including very young children, can try on the robes and possibly become chief.
Make sure you try with every villager, too - it's easy to forget the ones hiding in the ocean or answering nature's call. The easiest way is to pause the game and then drop everyone on the pedestal, I think.
Advice that Arthur gave in another post was to quit and restart the game app - occasionally the game doesn't choose the new chief immediately, but you can force it to do so by restarting (not your tribe, just the application

).