You can try changing your tables storage engines to InnoDB if MyISAM, if using MyISAM. If using MyISAM, you can also optimize tables with phpMyAdmin or similar tool. I discuss this in this post:
https://www.phpbbservices.com/2015/12/0 ... ge-engine/
But it could be the underlying issue is not in the database. If you are running PHP 5.6, an upgrade to PHP 7 will give you about 50% better performance. Make sure your version of phpBB can handle version 7 and make sure you know the maximum version of PHP supported by your phpBB version.
Upgrades in general can help, if you need an upgrade.
My signature line has a link to my site if you are interested in me looking into this.