We examine charmed-strange mesons within the framework of the constituent quark model, focusing on the states with L=1. We are particularly interested in the mixing of two spin-states that are involved in $D_{s1}(2536)$ and the recently discovered $D
_{sJ}(2460)$. We assume that these two mesons form a pair of states with J=1. These spin-states are mixed by a type of the spin-orbit interaction that violates the total-spin conservation. Without assuming explicit forms for the interactions as functions of the interquark distance, we relate the matrix elements of all relevant spin-dependent interactions to the mixing angle and the observed masses of the L=1 quartet. We find that the spin-spin interaction, among various types of the spin-dependent interactions, plays a particularly interesting role in determining the spin structure of $D_{s1}(2536)$ and $D_{sJ}(2460)$.
