The sublimation Polyester fabric recycling has been developed using the clear plastic water bottles, or PET as the raw material, a source of plastic that would otherwise go into landfill. For example, textiles such as fleece, are made from recycled polyester which is used by outdoor clothing manufacturers. Patagonia, Marks&Spencer and other fashion brands are very well known for using recycled polyester in their products. Teijin is a company in Japan who developed their own polyester recycling system back into polyester fabric, for re-use as clothing.
However, that is not always the case. Sometimes garments are not only made from polyester, but together with some other materials such as cotton. Therefore it makes the recycling process very difficult and even impossible.
“In some cases, (recycling polyester) is technically possible, for example blends with polyester and cotton. But it is still at the pilot level. The challenge is to find processes that can be scaled up properly and we are not there yet” stated Karla Magruder, a textile professional and the founder of Fabrikology International in her article on Suston Magazine.
So, yes polyester is recyclable, but a very large amount of polyester cannot be recycled although many institutions are working on a solution however a scalable one hasn't been found yet.