Speaking of rights in the context of Universal directories using, there are 3 main user types working with the application:
Directory admin (=Jira Admin) – configures the app, manages directories settings. All settings and tips descriptions are available in the relevant section of the documentation.
Directory users (=Jira users) – Jira users who can work with directories within the Directories section and/or within issues (according to their permissions) using the special custom field.
Other users – users with no access to the Directories section. They can be your internal users or customers, they can still work with the Universal Directories custom fields.
At first, the Universal Directories application should be added to your Jira. Read how to find, add and manage the Server apps (Atlassian documentation). The Universal Directories Settings section will become accessible for a user with Jira Admin rights at the Jira Administration section. You can also use the system hotkey G+G to find the Universal Directories settings.
Grant yourself all the permissions to work with Universal Directories.