Appears "the way" to install the client, if you want to use hombrew, is:
$ brew install postgresql
psql (the client command line) will now be available to you (it also installs a local Postgres server/database, but you don't have to use that if all you want is the client).
Apparently there's also a 'wrapper' to psql to make it more "user friendly" also available via homebrew (
brew install pgcli) in case interesting.
Pgcli is a command line interface for Postgres with auto-completion and syntax highlighting.
Another option is to install the
libpq homebrew package, but you have to force-link it (which is discouraged these days)
brew link --force libpq
or add it to your PATH (which is encouraged), see the directions that homebrew says after installation.