This can start with the job description for the Process Owner.
The job description list responsibilities, authority, and tasks to be performed including the skills, knowledge, and behaviors required to perform these effectively and efficiently. This should be as specific as possible to avoid ambiguity.
Competency is defined as demonstrated ability to apply skills and knowledge.
A skills/knowledge/behavior matrix can be developed to track competence.
The responsible manager(s) to whom the Process Owner reports, should track and report progress on this matrix.