<p>In this paper, we introduce and develop the concept of Clairaut submersions within the framework of statistical manifolds. Motivated by the classical Clairaut relation for geodesics on surfaces of revolution, we begin by establishing necessary and sufficient conditions for a curve on a statistical manifold to be geodesics. We then derive the conditions required for a statistical submersion to satisfy the Clairaut property. We also examine these submersions in the setting of statistical Ricci solitons, highlighting their geometric implications. Lastly, we establish Chen’s first inequality for Clairaut statistical submersions, followed by concluding remarks.</p>