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

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Cause 1

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

The user must change the Resolve Issues Permission:

1. Project settings
2. Permissions
3. Resolve issues

Preview image:

Cause 2

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

Solution

Go to Jira Settings → Apps → Xray Settings → Miscellaneous, 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.  (Image Added If you have Project Settings enabled, please go to Project Settings >> Xray Settings and verify the same options there.)

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Link for related documentation:

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