Christopher Pike
Officer shards can be gained through the Premium Officer Chest, the Ultra Officer Chest, Elite Federation Chest, Common Wrath Recruit Chest, the Discovery Officer 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. They can also be obtained from Field Training Milestone rewards. Extra shards can be acquired through the Offers tab.
 
Marlena Moureau
Officer shards can be gained through the Premium Officer Chest, the Ultra Officer Chest, Elite Federation Chest, Common Wrath Recruit Chest, and the Crucible of War Officer Chest. Occasionally, more shards can be acquired through Rotational Ultra Chests. They can also be obtained from Field Training Milestone rewards. Extra shards can be acquired through the Offers tab.
 
Hendorff
Officer shards can be obtained from completing the Plan B mission. Also, shards can be gained through the Elite Federation Chest and the Common Wrath Recruit Chest. Extra shards can be acquired through the Offers tab. 
 
Mae Darwin
Officer shards can be gained through the Common Wrath Recruit Chest. Extra shards can be acquired through the Offers tab. 
 
Frank Leslie
Officer shards can be gained through the Common Wrath Recruit Chest. Extra shards can be acquired through the Offers tab.
 
Geoffrey Hadley
Officer shards can be gained through the Common Wrath Recruit Chest. Extra shards can be acquired through the Offers tab.