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Recently, Sun--Zhang have shown that the manifold underlyingÌýany Kähler--Ricci shrinker is a quasiprojective variety, admitting a so called polarized Fano fibration structure. They have furthermore defined a notion of K-stability for polarized Fano fibrations and formulated a YTD-type conjecture. In this talk, I will present a proof of oneÌýdirection of the conjecture in the asymptotically conical case: If aÌýmanifold M admits an asymptotically conical Kähler--Ricci shrinker then M must be K-polystable.ÌýThis talk is based on joint work with Charles Cifarelli.