Question on amending live specializations

Summary:

Trying to find the best practices for amending live specializations. Please see the below scenarios that we would like to clarify how these should work

Content (required):

Scenario 1: learner has completed the specialisation and it is marked as complete on their record. We add a course to the same specialisation to see what will happen

Outcome: nothing changes, learner remains at completed as expected - Is there a way to automate the colleague to receive the additional course to complete or do we need to reassign the specialization? These specialization is assigned using initiative is there a way for the initiative to pick this addition automatically?