when a new stakeholder is identified, what is the next step?

When a new stakeholder is identified, the first step is to add He/She to the stakeholder register.
Second step is to analyse the stakeholder using the power/interest grid which is a two dimensional evaluation system, with some limitations, the Salience model is another data analysis tool you can use in analyzing stakeholders, it introduces the concept of urgency and legitimacy . Lastly the 3 dimensional cube is a more sophisticated analysis technique it supports the mapping of stakeholders in terms of Interest (active or passive),Power (influential or insignificant ) and attitude (backer or blocker)

The essence of this analysis is to understand what their needs, expectations,interest,requirements or stakes are on the project so you can effectively engage and manage them to deliver the project objectives.