Nothing is stopping you in creating as many JIRA Agile boards as you want for your JIRA Project.
You can define whatever boards you want.
However, a Scrum board already represents a sprint. When you're in plan mode, you have a list of issues. When you start a sprint, the working view, is showing the sprint.
If you're talking about a Kanban board, then yes, you can set a board filter for "issues in sprint X", and it will mostly duplicate the working view of the Scrum board. But you'll need a new board or updated filter for each new sprint unless you get a bit more clever with JQL functions that might pull out "latest sprint"
If you're thinking of JIRA Core boards, it's much the same as a Kanban in theory, although I'm not sure you can run the JQL you'll need.
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