It is rare to encounter a complete self-starter on your team.
Just about everyone will stand around waiting for direction.
When you find yourself with a self-starter it can be a challenge to get them going in the right direction if you aren’t ready to have them start.
How I’ve handled self-starters in the past is to promote them positions where their willingness to start something directly moves the project planning forward.
If they are technical, you can assign tasks for prototyping and researching interesting new technologies.
If they are creative, get them brainstorming new user interactions and use cases.
If they are organisational, get them to help with the project management.
It is not the failure of the self-starter to move in the proper direction, it is the failure of the project manager to utilise them effectively.