One of the easiest ways to raise freelance rates is to raise them on new clients. At some point, though, you will need to raise freelance rates on current clients. After a while, as you become better at what you do, and as you land more gigs, you need to figure out how to boost rates on the clients you already have.
This is never easy, but it is doable.
First of all, consider planning for regular rate increases. When you go to raise freelance rates, it's unreasonable to expect a current client to suddenly be able to handle paying you twice your current rate. Consider revisiting the rate regularly, so that your clients can get used to small increases over time. This allows everyone to adjust.
Additionally, continue to use the practice of quoting higher rates to new clients. That way, when you reach the point that current clients aren't willing to pay more, you will be covered by higher rates elsewhere.
It's hard for me to raise freelance rates on current clients because so many of them are my friends. In some cases, the higher rates I charge new clients subsidize the rates I charge my friends and earliest clients. Sometimes, letting them pay a lower rate is worth it because they are easy to work with and familiar.