It depends on all the functionality you need. Not everything in JIRA is exposed via REST APIs and hence you might need a plugin in some cases.
I would recommend taking a look at existing products like ConnectAll (developed by my company) and see if that works for you. I know that it works between Cloud and on-Premise instances.
With Exalate, as you mention in your tags, yes. There are other sync type tools - Backbone and Connectall for example. In the wider world, some people are using non-Atlassian based tools such as IFTTT or Unito
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