Past tense,It same as "ed" in English~

"了" usually comes at the end of a sentence. In most cases, it carries a meaning of the English "ed" (as in the "ed" you add behind a verb to show past tense) or "already". I am native to Cantonese (not Mandarin) but I guess in your sentence's case, the sentence means "the office is on the 3rd floor, we go up to the building (floor), to get the library card fixed first"

I hate "了" grammar, I never understand hahaha. good luck with your studying Chinese!

相当于“完成”的意思

modern-Chinese does not have a marker for tense, and to tell learners otherwise is very misleading. Just take this as an example: 豬逃了怎麼辦？ It could mean "The pig has escaped; what should we do?" or "What should we do if the pig escapes?" Saying that 了 just indicates past tense is plain wrong.