Do you have a picture of the chair?
hometalk has some GREAT ideas...
A swing back or a wing back?
I did a partial recovering of a ripped wing back chair. It was so easy and after several years of heavy use, it's help up great. You can peek if you like. https://www.exquisitelyunremarkable.com/2015/07/custom-upholstered-chair-easy-diy.html