No. JIRA doesn't have any form of field-level security in it.
There are a couple of tricks you can play if you have Server versions of JIRA, including one add-on that is explicitly for it which works really well, but there's no options for it on Cloud.
Remove the field from the "edit" screen and it will become read-only (leave it on the "view" screen of course).
That blocks all edits though, so you might want to consider having it on transition screen and having transitions that then use conditions to only allow certain users to perform them.
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