Where do I find me a new ship?

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I want my Lt. to fly another vessel for his rank. Where in Earth Space Dock do I go to requisition one?

[Archived Post]

If I understand your question correctly, the shipyard.

[Archived Post]

There are no other ships at Lt rank just the starter ship.
At Lt Commander you will be given a ship of your choice for free. After which you can buy the other 2 at 20,000 each. From the Ship Requestion floor, you get there by going in the turbo lift on the first floor of the shipyard.

I have all 3 ships at Lt commander 4. I took the science ship free and bought the other two, the cruiser and the escort for 20,000 each, money I got from just doing quests.

[Archived Post]

I am currently commanding a Constitution Class Starship.