Alexander Marcus
Officer shards can be gained through the Premium Officer Chest, the Ultra Officer Chest, Elite Federation Chest, and the Crucible of War Officer Chest. Occasionally, more shards can be acquired through Rotational Ultra Chests. You can also exchange Transporter Patterns for extra shards.
 
Yuki Sulu
Officer shards can be gained through the Premium Officer Chest, the Ultra Officer Chest, Elite Federation Chest, and the Crucible of War Officer Chest. Occasionally, more shards can be acquired through Rotational Ultra Chests.
 
John Harrisson
Officer shards can be obtained from completing the following missions: Misdirection and Uncaged. Also, shards can be gained through special events and Elite Federation Chest. Extra shards can be acquired through the Offers tab.
 
Paul Zhou
Officer shards can be gained through the Premium Officer Chest, Elite Federation Chest, and the Crucible of War Officer Chest.
 
S31 Zeph
Officer shards can be obtained from completing the Rough Business Part 5 mission. Also, shards can be gained through the Refinery. Occasionally, more shards can be acquired through Event Store.
 
S31 Alok
Officer shards can be obtained from completing the Divide and Conquer Part 6 mission. Also, shards can be gained through Event Rewards. Occasionally, more shards can be acquired through Event Store.