n. A sport that involves climbing a mountain and then descending using a paraglider or similar craft. [paragliding + alpinism]
paralpine adj.
paralpinist n.

Example Citations:
New sports continue to evolve, as outdoor athletes combine things like climbing and BASE jumping, and alpinism and paragliding (paralpinism).
—“The aerial revolution,” Explore Magazine, February 21, 2012

Europe is leading the world in paralpinism. There attitudes toward human flight are encouraging the development and practice of some of the most incredible feats in the history of human flight and paralpinism.
—Walker Mackey, “The Adventures of Dr. Frankelton,” Vertical Exploration, August 4, 2012

Earliest Citation:
I am seeking a simple calculation or graph which will relate the effect of wind speed with altitude.
—irwyn, “Paralpinism: Wind speed,” Paragliding Forum, October 11, 2007

I found another citation, which might be the earliest, or it might be quite recent. It’s an English translation of a German account of an apparent paralpine expedition that occurred in November, 1999. The problem is that the “translation” seems only marginally related to the original text, including (crucially) its use of the word paralpinism, which doesn’t seem to appear in the original (although I don't speak German). That said, the word does appear in the translation, so it qualifies as a cite, but it’s not possible to say when the translation occurred: it could have been just after the expedition, or it could have been 2013, which is the page’s copyright year (not that that means very much). Anyway, here’s the cite:

His feat is a highlight in the increasingly popular sport of “paralpinism“ which seeks to combine paragliding and mountain travel (whether climbing, skiing or hiking) in a single outing.
—ThinRedLine, “Ama Dablam (6856m) 3. November 1999,” Flug Schule Salzkammergut

Here’s another problematic cite that has an older (albeit known) date, but refers to the name of an organization, so it’s not clear whether it’s a reference to the sport or just a clever name someone thought up:

Try ‘Paragliding’ in large metropolitan Yellow Pages, or failing that, get in touch with local hang gliders and ask them. Or, you could always come out to Vancouver and learn from First Ascent Paralpinism.
—new england parachuting, “SKYDIVE,” rec.skydiving, September 25, 1992

Related Words: