Old Version

Assuming the plugins you need work in 2.8.4, then you should be able to upgrade.

Best results have been reported by upgrading in incremental steps, though in theory you should be able to go directly from 2.1.3 to 2.8.4.

Incrementally, upgrade 2.1.3 to 2.2, 2.3 to 2.5, 2.5 to 2.6, 2.6 to 2.7, 2.7 to 2.8. That last step can be done automatically with the native upgrade in Tools->Upgrade.

Review Upgrading WordPress.

Thanks, Michael. How can I tell if the plug-in works in the current version — given that it hasn’t been updated for some time?

Could ask the plugin author or look at the compatibility pages.

https://codex.www.ads-software.com/Plugins/Plugin_Compatibility
https://codex.www.ads-software.com/Themes/Theme_Compatibility

Also see the Migrating Plugins and Themes to x.x pages listed under the M here:
https://codex.www.ads-software.com/Category:Advanced_Topics