No, no, no!
Nope, not leather, wood.
What you want is a nice, strong, thin slat of wood you can either curve ahead of time with heat or steam, a scrap piece of osage or ipe, maybe, OR multiple thin layers so they conform to the curve you want on the recurve.
You sand or plane out the cracks on the belly side of the curve, or at least down in to the wood, making it very flat and squared up, then glue the slat on to the belly to reinforce the recurve, basically replacing the wood you had to sand out, and then some. Then you trim any extra and smooth in the transition so you don't leave a stair step where your recurves start.