You don’t mention what aero road bike you have, so it is kinda hard to give any feeling re: that frame vs. the Cheetah.
That said, the Ridley is nothing special for an aero design POV. As others noted, the gain will be from being able to get in a better position.
Also, a TT bar set-up is more aero than drop bars with clip-one. Further, if you swap out the round base bar for something like the Zipp Alumina Vuka base bar, you can save a few watts there. The Vuka is pretty cheap and would be a worthwhile investment. Obviously a carbon aero base bar would be even better, but also $$$.
A TT frame will have a lower stack and long reach (generally) than a road frame. So you would be able to move farther forward without having to run a long stem and potentially be lower than your road set-up.
That said, I ran a converted Cervelo S2 as my Tri bike for a few years and was every bit as aero on that bike as I am now on my Shiv TT. Had to get a -17* stem however to get low enough…but it can be done.