The first questions is obviously to identify why someone is not performing. It is important to focus on outcomes rather than outputs. If this person is doing everything wrong and is getting outstanding results, then stay out of the way and learn.
If someone is not carrying out a task and this has no impact on standards, maybe you need to promote this person. There is no point doing well what is not worth doing. A lot of schools have, for example, complicated lesson management and book marking policies. These do not always have a bearing on outcomes.
When not carrying out a task such as marking properly (identifying what needs to be done in order to reach the next stage rather than corroborating that something has been done) is obviously having an impact on standards, then this is clearly a training issue. Your colleague does not do something which will have a positive impact. This is a problem.
Obviously, there is some convincing to be done. This is a management issue and does not relate to non-performance.
You will obviously convince this person that they have to do it and they will do it. If they still refuse then get them to agree that you view has at least some validity. Once there, it becomes a set of clear instruction they have to abide.
If they do not then they are a non performing colleague… Just do not jump the gun and accept that there are a lot of reasons why someone is not performing...