Trying to find the setting for resticing who can start or complete a sprint to only a group of users.
I locked down who can "manage" a sprint but it does not lock down the start or complete buttons. for none admin's or leads of that project
Manage Sprints permission should have done it for you. Are you using JIRA cloud or server?
https://confluence.atlassian.com/adminjiracloud/managing-project-permissions-776636362.html
If you're on an older version of JIRA Software, you may not have that permission, it's a relatively recent addition.
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