We study the dual ${ \rm G}^\ast$ of a standard semisimple Poisson-Lie group ${ \rm G}$ from a perspective of cluster theory. We show that the coordinate ring $\mathcal{ O}({ \rm G}^\ast)$ can be naturally embedded into a cluster Poisson algebra with a Weyl group action. We prove that $\mathcal{ O}({ \rm G}^\ast)$ admits a natural basis which has positive integer structure coefficients and satisfies an invariance property with respect to a braid group action. We continue the study of the moduli space $\mathscr{ P}_{ { \rm G},\mathbb{ S}}$ of ${ \rm G}$-local systems introduced in \cite{ GS3}, and prove that the coordinate ring of $\mathscr{ P}_{ { \rm G}, \mathbb{ S}}$ coincides with its underlying cluster Poisson algebra.
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