It is possible to install or update GrumPHP on your system with following commands:

composer global require phpro/grumphp

This will install the grumphp executable in the ~/.composer/vendor/bin folder. Make sure to add this folder to your system $PATH variable:

# .zshrc or .bashrc
export PATH="$HOME/.composer/vendor/bin:$PATH"

That's all! The grumphp command will be available on your CLI. When your project also has a grumphp executable, this on will be used in favour of the one globally installed. The same goes for other tools like e.g. phpunit you have installed both globally and locally.