Emperor Georgiou
Officer shards can be obtained from completing the Holo-Program: Avenge Them mission. Also, shards can be gained through the Discovery Officer Chest and Ultra Recruit Chest. Occasionally, more shards can be acquired through Rotational Ultra Chests.

Captain Tilly
Officer shards can be gained through the Discovery Officer Chest and Ultra Recruit Chest. Occasionally, more shards can be acquired through Rotational Ultra Chests.

Lorca
Officer shards can be gained through the Discovery Officer Chest (only with the Discovery Refit), the G4 Rare Armada Pack in the Alliance Store, and Ultra Recruit Chest. Occasionally, more shards can be acquired through Rotational Ultra Chests. Extra shards can be acquired through the Offers tab.