The Gemini-Era Spacesuit is a piece of clothing that can be obtained from the Mothership Zeta DLC. The player obtains it after awakening the people from different time periods who are trapped in a stasis lockdown. It is directly after completing the Not of This World quest.
When you awaken them, the astronaut will die almost immediately. Looting his body will allow you access to the Spacesuit. Without it, you cannot complete the Among the Stars quest and you aren't able to access the Space Walk.