No. If you are able to qualify for a private refinance loan on your own, you can combine your existing student loans into the new refinance loan without a cosigner. This will pay off your existing loans, and create a new loan solely in your name. Releasing your cosigner of any obligation.
However, if you are unable to qualify for a private refinance loan on your own, you may need a cosigner—but this cosigner could be someone else, it doesn’t have to the be the same cosigner you used previously.