None that I'm aware of (or can find on DARPA's site). DARPA might help a PM maintain their clearance if they already have one, but I don't think they require one for new PMs (unless the project directly requires classified information, which of course some do).
@throwawaylol_ is correct. I'm afraid you're mistaken.
I saw your other comment as well, thanks.
(I don’t know why ‘throwawaylol_ is flagged; I vouched for their comment.)
In talks, Mudge has referenced participation in various Pentagon projects that would definitely require a nontrivial clearance.
I'm not doubting so much as asking curiously: I've participated in what I'd guess are fairly sensitive Pentagon projects (commercially, over about a year and a half†) and I've never been cleared for anything.
† None of it involved vulnerability research; this was back in my anti-DDOS days.
Same, except I was directly involved in vulnerability research and mitigation and didn't need clearance. You only need a clearance if you are directly privy to information requiring said clearance.
That would depend on the project, and what aspects of it you might be involved in.