On my MacBook Pro with macOS Mojave, my version of zsh is 5.3.

zsh --version

zsh 5.3 (x86_64-apple-darwin18.0)

That version is a few years out-of-date, according to this. That page shows version 5.7.1 being current.

➥ Is there some way to update to the current version of zsh?


Not exactly. You can't (although that can be overridden) and should not update anything in /bin as that is controlled and updated by Apple.

However you can install zsh from elsewhere and put it in another place and use that path to start it from Terminal.

One way is to download the source from here and compile it.

However it is probably easier to install from a package manager like Macports or Homebrew both of which will have compiled up the binary.