Not a single word, but planetary meteorology seems to fit the bill (as opposed to terrestrial meteorology). It requires some particular reading of the words though (ie, planetary to mean non-Earth planets, and terrestrial to mean Earth), but it has been done. See, for example, https://global.jaxa.jp/article/special/explore/imamura02_e.html
Japan is one of the leading countries in the field of terrestrial meteorology. With that background, I believe that we can lead the research of planetary meteorology as well.
Another candidate is extra-terrestrial meteorology. See, for example, https://www.worldcat.org/title/horizon-the-weirdest-weather-in-the-universe/oclc/1089752078
Now scientists have started looking to the heavens and wondering what the weather might be like on other planets. Today, we are witnessing the birth of extra-terrestrial meteorology, as technology is allowing astronomers to study the weather on other planets like never before.
So just as investigating Earthly weather can tell us about processes occurring on other planets, delving into extra-terrestrial meteorology can shed some light on how our own atmosphere does, or does not behave.