Thank you for your question.
I can confirm that ScriptRunner for Jira Server comes with the Hide UI Element Built in Script as described inside of the documentation page located here.
You will be able to take this built in script and configure it to hide issue linking panel on an issue so that users cannot remove the issue link.
You will then be be able to add a Behaviour on the edit screen to make the field read only when a user edits the issue to stop users from editing the field and to only users in a certain group or project role to edit the field as described in the documentation page here.
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