How would a Public Relations professional with experience in the non-profit sector make a career move to the private sector?

Resume overhaul. If you have friends working in-house I would select a few of them to review your resume and provide their honest feedback. Everyone wants to feel important these days so if you communicate your desire to work in-house and ask for their advice you'll be pleasantly surprised at how much info them provide.

Update your Linkedin profile to highlight your skills, abilities and knowledge - with a sharp focus on your experience.

Focus on what type of in-house role you seek, then contact those people and ask to meet for a coffee (a bit old school, but it still works)

Social Media is important for inhouse roles, so be sure to maximize your profile across all platforms. If you are private on Instagram I would suggest creating a public profile that is focused on the field you desire.

Build your connections. In-house roles come and go, so its important to know who makes the decisions and become friends with those people.