The newly introduced function "CurryApplied" (https://reference.wolfram.com/language/ref/CurryApplied.html) may fit your need. CurryApplied[A,{2,1}][G] is exactly what you want.

For example:

Input:
A[F_, G_] := D[F, x] D[G, y];
Print[CurryApplied[A, 2][x][y^2]];
Print[CurryApplied[A, {2, 1}][y][x^2]];
Print[CurryApplied[A, {2, 1}][x^2][y]];
Output:
2y
2x
0