Private practices aren't necessarily connected to doctoral programs, generally, although occasionally faculty would provide a referral to an alumnus if students were seeking outside therapists. That's about it at my alma mater. I'm in private practice several states away from my grad program.
Much more commonly, folks leave the state for internship and/or postdoc and then decide where to settle based on different factors (spouse/family, connections, jobs, etc.).
You probably shouldn't rely on a grad program to get you set up for private practice referrals. Instead, you need a niche that a particular community is in need of (working with kids, DBT, forensic assessments, postpartum depression, men's issues, etc.) and that takes research/exploration, and belonging to county psych associations and networking there. You are way ahead of yourself at this point, but you can certainly look into specialties you're interested in.
Private practice is a huge, risky, and expensive undertaking, so scour the private practice threads in here first to learn more and google some private practice blogs to see more info. After that, if you have specific questions, you can PM me.