Burnham
Officer shards can be obtained from completing the following missions: Swings and Roundabouts Part 1 and Part 5. Also, shards can be gained through the Discovery Officer Chest, Ultra Recruit Chest, and exchanging Transporter Patterns. Occasionally, more shards can be acquired through Rotational Ultra Chests.
Saru
Officer shards can be gained through the Discovery Officer Chest and Ultra Recruit Chest. Occasionally, more shards can be acquired through Rotational Ultra Chests and Event Rewards.
Paul Stamets
Officer shards can be obtained from completing the following missions: Swings and Roundabouts Part 3 and Part 5. Also, shards can be gained through the Discovery Officer Chest and Ultra Recruit Chest. Occasionally, more shards can be acquired through Rotational Ultra Chests. Extra shards can be acquired through the Offers tab.
Georgiou
Officer shards can be gained through the Discovery Officer Chest. You can also exchange Transporter Patterns to get additional shards.
Tilly
Officer shards can be obtained from the Discovery Officer Chest.
Tyler
Officer shards can be gained through the Discovery Officer Chest and Ultra Recruit Chest. Occasionally, more shards can be acquired through Rotational Ultra Chests.
Hugh
Officer shards can be obtained from the Discovery Officer Chest. Extra shards can be acquired through the Offers tab.
Airiam
Officer shards can be obtained from the Discovery Officer Chest.