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More than likely you will need additional core licensing. Not sure what version of Tableau Server you're running but often with a 3 node cluster folks will have one Primary and two Workers. Often the Primary won't be running any "licensed services" but can run "non-licensed" services such as Gateway which means the cores for the Primary won't count towards your overall total. But let's say both Workers are 8cores each and they're both running VizQL and Backgrounder processes (which are licensed) this would mean you'd need a 16core license in total.
In the link to OnlineHelp below if you scroll down you'll find a table that lists out the different Tableau Server processes, what they do and the last column is if it's considered a "Licensed" process or not.
How much does it cost for additional 8 core Server licence?