The canonical term for an ‘independent’ priest is vagus.
There used to be a smattering of these since the seventies. Basically they were conscientious objectors to the liturgical reforms.
I suspect however that there will be fewer of them since the Motu Proprio. Cardinal Castrillon Hoyos has made it a priority to reconcile these priests with the hierarchy. Many have died in recent years, and obviously could not create their own replacements.