Reach out and ask them: "do you know anyone who needs some help? We have some availability coming up." This lets them think about who in their network might need some extra hands (or if they themselves need help) without putting them on the spot.
Don't only ask your current contact at past clients, but also anyone you worked with. LinkedIn is your friend here.
You don't need a formal referral program, but it is much easier to work with someone you've worked with before rather than convince someone who doesn't know you that you can solve their problems.