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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 obtainedTalenti-type comparison theorem is sharp, rigid and stable with respect tomeasured Gromov-Hausdorff topology. As an application of such Talenti-typecomparison, we establish a sharp and rigid reverse H\"{o}lder inequality forfirst eigenfunctions of the $p$-Laplacian and a related quantitative stabilityresult.

A Talenti-type comparison theorem for the $p$-Laplacian on $\mathrm{RCD}(K,N)$ spaces and some applications