Most space suits are developed by governmental space entities like NASA, Roscosmos, JAXA, etc; or, through a government contract with a commercial developer. If you really want to get into the market of space suits, I can hit some key points for you:
Typically the work is by government contract or for a commercial space launch company like SpaceX
The market is very limited regarding space suit development
There are currently jobs available and there is potential for future growth/need for space suits
Additional space suits will need to be developed for the handful of upcoming space stations being planned, lunar missions via NASA's Artemis, and other potential human space flight missions
Commercial space suit developers
Is anyone looking for people to work on space suits? Absolutely. Here are some places with calls out to people.
European Space Agency - Design A Spacesuit - March 2, 2023
SpaceX - Job Opening: Space Suit Sewer ($70-90K year)
SpaceX - Job Opening: Space Suit/Crew Equipment Engineer ($95-130K year)
KBR - Job Opening: Space Suit Program Support Technician ($44-67K year)
KBR - Job Opening: Space Suit Sewing Technician ($not listed)
Oceaneering - Job Opening: System Safety and Reliability Engineer, Space Suit and Lunar Operations ($not listed)
There were a lot more listed when I googled “space suit jobs”
What sort of skills does someone need for space suit construction?
Industrial sewing, especially with high-level textiles
CAD, 3D modeling, mathematical modeling
Pattern-making
3D Printing
Engineering degree - For the mechanical and electrical aspects of the suit, possibly materials engineer
Theater, Costuming degree - For the literal designing, sewing, pattern-making, and construction of the suit
Computer Science degree - For the integrated computer system that might be included in the suit
Aerospace Engineer degree - Someone proficient with a PLSS system - creation, integration, testing
Business degree - Project management, logistics, purchasing, project accounting, project coordination
Smith Aerospace Garments talks to Orbital Assembly
NASA unveils Artemis mission space suit
NASA’s next-gen space suit
SpaceX space suit vs NASA space suit
Links:
NASA TURNS TO COMMERCIAL PARTNERS FOR SPACESUITS by Tom Nardi, Hackaday - June 3, 2022
Making a Sexier Spacesuit by Daniel Oberhaus, Slate - October 7, 2015
Here's every key spacesuit NASA astronauts have worn since the 1960s — and the new moon suit it just unveiled by Dave Mosher, Jenny Cheng, and Bianca Giacobone, Business Insider - March 16, 2023
New Moon Suit for NASA’s Artemis Astronauts Unveiled by Kenneth Chang, NY Times - March 15, 2023
Designing a More Inclusive Future for Space Exploration by staff at Morgan Stanley - October 25, 2022
Under Armour designs pilots' spacesuits for Virgin Galactic's first commercial spaceflight by Natashah Hitti, Dezeen - December 6, 2020