We've discussed upgrading the Zabbix server. But there're quite a lot of components, and the compatibility between each of them differs slightly. Actually, the official compatibility rule list is very short:

• All older versions of Zabbix agents are supported but, starting from Zabbix 4.0, agents older then 1.4 aren't supported anymore.
• Zabbix server, proxies, and Java gateways must be of the same major version.

Regarding the agents, it really is as great as it sounds. All of the old agent versions will work with the latest version of the Zabbix server or proxy, even down to 1.4—with versions older than 4.0, even back to version 1.0 from 2001. If you upgrade Zabbix server, you can keep your agents as is; although you wouldn't benefit from new features, performance, or even security improvements.

Technically, combinations outside of the support rules might work. For example, a more recent agent might work with an older server in some cases, and the Zabbix Java gateway protocol hasn't changed much, so it's likely to work with different major versions of Zabbix server, too. Such combinations aren't tested by Zabbix developers, aren't supported, and should be avoided in general.