You can add new picklist options to an existing field by navigating through setup and editing record types.

1. Navigate to Setup > Create > Objects.
2. Click the object name.
3. In the Custom Fields & Relationships section, click the field.
4. In the Picklist Values section, click New.
5. Type the new options values.
6. Select the Record Type Names specified in the table provided in this article.
7. Click Save.
8. Check if the new options are listed in the Picklist Values section.