As admin, if you intend that only a group of users should have access to Xporter. You can follow these steps below.

Step-by-step guide

Go to Jira settings > Apps > Xporter > Global Settings (Server/DC) or Miscellaneous (Cloud) > Global Permissions > disable this option "Enable Xporter for all projects and all users"

Product Support Knowledge Base > [Xporter] Do not allow all users to use Xporter > Xporter permissions.png

2. Go to Jira settings > Apps > Xporter > Permission Schemes and ADD a new one:

Product Support Knowledge Base > [Xporter] Do not allow all users to use Xporter > xporter permisisons2.png

3. Go to Edit your Permission Scheme:

Product Support Knowledge Base > [Xporter] Do not allow all users to use Xporter > xporter permisisons 3.png

4. Here you can define which issues types are allowed to be exported, define which project roles are allowed to use Xporter for Jira, define which user groups are allowed to use Xporter for Jira, associate templates to certain issue types:

Product Support Knowledge Base > [Xporter] Do not allow all users to use Xporter > image2019-4-26_18-5-20.png

5. You can also go to the "Project" option:

Product Support Knowledge Base > [Xporter] Do not allow all users to use Xporter > Xporter permissions 4.png

6. And here you can Assign projects to your Permission Schema:

Product Support Knowledge Base > [Xporter] Do not allow all users to use Xporter > image2019-4-26_18-6-57.png

Link for related documentation

Check this documentation to find more information about Permissions Schemes, here