2% ire chance, there is no other way to trigger it than by killing elites.
If you want only to use one Shard, I would suggest first at least drawing an Ire if not spawning the Herald in the current TZ, and then Sharding an Act that doesnt have the TZ that yiu just cleared.
Also I would suggest looking at whuch is the next TZ and nit that the Act that it will be in.
This will give you 2 TZ + one full act, and if you do first TZ clear at XX:55 or XX:25 you can then hit the two TZ, look at next TZ, giving you 3 TZ + Full Act. If you are not very fast at clearing full Act and can handle a bit of idling (maybe gambling or stash management or rolling charms or whatever IRL activity) you can get a 4th, this one you will go in the dark while popping shard tho so it may be in the Act you sharded.
Anyways, I would suggest not popping a shard unless you at least already drew an Ire. Your full clear was unlucky tho