Depending on the project configuration, a project administrator might be able to perform some tasks,...

A project administrator can remove watchers from project notifications, if they have the Manage Watchers permission. This is a task that does not require Jira administrator access, and can be done by the project administrator from the issue view. Removing a priority value used by the project, updating permissions for a project user, and limiting who can bulk edit project issues are all tasks that require Jira administrator access, and cannot be done by the project administrator. References: Managing watchers, Managing Jira Projects Data Center and Server: Certification Bundle