This article will help when a user doesn't have permission to execute a Test. 


Check in the image above the associated error:

Cause 1

The User does not have the necessary issue permissions: "Browse" and "Resolve"


Go to Project Settings → Permissions → Project Permissions:

Cause 2

The Test Execution issue is not in a Status configured to disallow executions.


Go to Administration → Add-ons → Miscellaneous, under the "Workflow Status" section, to the option "Disallow executions of Tests with workflow statuses," and check if you have any status that does not allow users to execute the Test:

Cause 3

The Test Executions are restricted to the assignee user.


Go to Administration → Add-ons → Miscellaneous, on the "Test Run Options" section; the third one may be activated "Restrict tests execution to assignee," disable this option to allow all given users to be the Test Run assignee:

Check here for more information.