"something past primary school" vs "something passed primary school"

Not a native speaker. I realized that I don't know which word to use in the following sentence:

I have never suffered a broken leg past primary school.

Or

I have never suffered a broken leg passed primary school.

Wecome to EL&U.

"Passed primary school" means either that you achieved an academic score which allowed you to progress beyond primary school (that is the equivalent of "passed the baccalaureate" for secondary school) or that you drove or walked past the primary school building.

"Past primary school" is closer to what you intend but is not the most common way to speak of something other than academic study. For instance it would be normal to say "I have not studied Spanish past primary school level" but not "I have not had a broken leg past primary school"

For almost anything else, including even academic study in many cases, the most normal form would be "Since primary school" so, in the case of your example, you would say "I have never suffered a broken leg since primary school". Even more common would be "I have never suffered a broken leg since I was at primary school". The first of these two forms is rather more likely to used to talk about something which was part of the school routine so you might say "I have never learned Spanish since primary school". The point is that a broken leg is a single occurrance which is not (in most schools anyway) a part of the school curriculum or the school routine and the connection between the broken leg and the school is that the fracture happened when you were at primary school, not necessarily because you were at primary school.

The best way to say what you originally posted is "I have never suffered a broken leg since I was at primary school"