Ath'kethin
Elder Thing
Have a few adventures, a plot will emerge. It isn't always wise to start with a big campaign arc planned out, because that can lead to railroading.
Stay true to Conan and run episodic adventures?
Here you go. I've run Sword & Sorcery adventures/campaigns pretty exclusively since 5e came out, and this is the way to do it.
Not every campaign needs an overarching plot, and if you DO need one your players will hand it to you after an adventure or six.
Don't sweat it. Just play.