  In this paper, we prove a Talenti-type comparison theorem for the
$p$-Laplacian with Dirichlet boundary conditions on open subsets of a
$\mathrm{RCD}(K,N)$ space with $K>0$ and $N\in (1,\infty)$. The obtained
Talenti-type comparison theorem is sharp, rigid and stable with respect to
measured Gromov-Hausdorff topology. As an application of such Talenti-type
comparison, we establish a sharp and rigid reverse H\"{o}lder inequality for
first eigenfunctions of the $p$-Laplacian and a related quantitative stability
result.
