You can use the quilt as the batting for a new quilt. Back when.. often there were mulitple layers of quilt tops and backs on the same quilt. Depending on the fiber content and density a long arm quilter may be able to apply the new top ( it can be just a single cut of fabric) and backing . and quilt it so it can lay flat. Depending on the colors of the quilt you have .. it may restrict what your color choices are for a new covering and backing , so the old does not show through. What are the measurements of the quilt.
A photo would help in guiding you.