Once you've obtained a new Ship, you'll need to learn more about it in order to optimize its capabilities.
Continue to collect Ship Schematics for that ship in order to apply new levels to it. Depending on the Quality of the Ship, you might be able to procure Schematics in a variety of ways.
For Common and Uncommon Ships, you can accumulate Schematics as rewards for completing certain Away Missions and Ship Battles, as well as claiming Daily Rewards.
For Rare or better Ships, you can win additional Schematics from the Battle Arena, Dabo Wheel, or from the Premium Time Portal pack. There will also be occasional packs and offers that are entirely comprised of Ship Schematics, and provide a higher chance of Schematics for a Specific Ship.