At the project Permission Scheme, you are able to configure many different permissions.
You need to make sure that users are going to create Xray issue types (such as test, test plan, test executions & test sets) and that the executed tests have at least the following permissions:
Browse Projects
Ability to browse projects and the issues within them.
Create Issues
Ability to create issues.
Link Issues
Ability to link issues together and create linked issues. Only useful if issue linking is turned on.
Resolve Issues
Ability to resolve and reopen issues. This includes the ability to set a fix version.
Add Comments
Ability to comment on issues.
Create Attachments
Users with this permission may create attachments.
You may also consider other permissions such as:
Assignable User
Users with this permission may be assigned to issues.
Assign Issues
Ability to assign issues to other people.
To configure the Project Permission Scheme, go to Jira Administration Settings > Issues > Permissions Schemes.
Select the project permission scheme you want to change and select "Grant Permission."
If you want your users to be able to configure test & test steps status, test types, test environments and even configure test coverage and defects mapping you need to give them "Administer Project" permission.