In 4.0 you no longer need Font Awesome for the default box types shipped with Premonition. So if you only have been using the default stylesheet, then it should be ok to remove Font Awesome from your site, as long as you install the new stylesheet.
In your Gemfile, make sure to upgrade Premonition itself
gem 'premonition', '4.0.0'
Run
bundle update
Make sure to delete your old premonition (s)css file. Install the new premonition.scss SASS stylesheet
bundle exec jekyll premonition-install
The default template has changed in 4.0, in order to support the new default icons AND Font Awesome.
The main change is on how we include icons
<i class="{% if meta.fa-icon %}fas {{meta.fa-icon}}{% else %}premonition {{meta.pn-icon}}{% endif %}"></i>This might require some figgling on your end. So sorry about that!
Post an issue if you run into probems with this.