How do I improve a team member capability to perform a process?

You improve at the task level. Level 3 is the level that is regarded as ‘capable’
So you identify the tasks that the team member is <3 then prioritise which of them you train and coach the team member to reach level 3 rating.
You should tag each process or task with a volume. Doing so will allow you to sort the matrix by volume, therefore enabling you where to identify areas of skills growth potential for the most frequent tasks/processes. This will help you to ensure training is provided against the highest volume tasks.