下す is not a word you’re going to encounter all that often.
It’s labeled as a “common word” on Jisho, but there are 21000 entries there with the same label. Most people aren’t thinking that broadly when they imagine “common” words.
I can’t honestly remember the last time I heard someone use it in everyday speech, if it’s ever happened at all for me.
It’s possible that the abstract usage of “to hand down” as in “to hand down a sentence” or “to pass judgment” might show up if you read crime newspaper articles.
Anyway, 下げる is absolutely a beginner word, something you need in your first 500-1000 words. 下す might be in your first 21000, but I wouldn’t sweat it.
EDIT: And one more thought… this reminds me of when I first started learning Japanese and I had no idea of what associated words were good to know and which ones could wait. So I was frequently overwhelmed with things like 下 and 生, because lots of resources don’t even try to tell you what the frequencies of various readings are. くだ is a great reading to know for 下, but not because of the word 下す. You need it for 下さる (and by extension, 下さい). The word 下り will also show up if you ride trains in Japan.