How to get the Zealous trait

You can only get Zealous as an adult via events, which are never guaranteed to fire. You can go on a pilgrimage or hope for an event while educating your ward.

To expand though, you're probably going to have to do it the old-fashioned way: use your Chancellor to forge claims on neighbouring titles, or marry members of your dynasty into titles that their children can inherit later, and then press them in war. Expansion via conquest is really easy but it spoils you like candy: it makes the normal, slow, and strategic expansion that is the mainline gameplay of CKII seem really, really slow. However, that's as it should be?—?every ruler plays by the same rules, and that slow expansion protects the stability of your borders as much as it prevents you from biting off big chunks of your own neighbours' realms.

Assuming you have the Way of Life DLC there is one guaranteed method to become Zealous. (I will also assume nothing in Elder Kings disables anything relevant from Way of Life)

If you pick the Scholarship Focus it creates a new Decision to "Build an Observatory." It costs 50 gold and initiates a roughly 5 year long event chain. Once built you have to choose to study the movement of the stars. The full event chain is detailed here. The short version is you must continue to press onward in spite of any obstacles that come up until you finally have a major breakthrough in your studies. At this point you will have the option to publish your findings, keep them secret or burn your discovery. Burning your discovery makes you Zealous.

Failing that, it's largely a matter of hoping the right random event fires that gives you a shot at becoming Zealous.