Not in the way you describe, because boards do not belong to projects, they are independent of them.
You can set the board sharing so that they are only available to certain people, and if a board includes a project that a user cannot see, it will not expose any of that projects issues to them when you use the board.
But it's quite hard to think of board access at a project level. Check the options for who you can share a board with.
Hey Atlassian community, I help lead engineering at Sentry, an open-source error-tracking and monitoring tool that integrates with Jira. We started using Jira Software Cloud internally last year, a...
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