To view, add or change acceptance criteria on Jira issues you will need to have the, "Edit Issue" permission in Jira. This process differs depending on whether you are using a company-managed or team-managed project, below is a guide on how to enable this.
In a company managed project, various roles may have the, "Edit Issues" permission, to view which roles have this permission, go into the Project Settings.
From here, you can move to the Permission settings menu and scrolling down to the Issue Permissions section you should be able to see the Edit Issues permission. To the right of this it will show the individual Users, Groups and Project Roles that have this permission. You will either need to put the user needing access into one of these roles or alternatively expand their role to have this capability.
For a team managed project you can see the members who have, "Edit Issue" permissions by going into the Project settings.
In the Access section of the project settings, you can see individual members of your team and the Role they currently have. By default, Jira adds the Administrator, Member and Viewer roles; of which the Administrator and Member will have the Edit Issue permission. If you have your own custom roles, these can be changed to have Edit Issue permissions from the Manage Roles section in the top-right.