Presheaves of $k$-morphisms associated to fibred $\infty$-category

Question

In category theory one has presheaves of morphisms associated to fibred category as follows. Let $p : \mathcal{D} \rightarrow \mathcal{C}$ be a fibred category. Let $U$ be an object of $\mathcal{C}$ and $x$, $y$ objects in $\mathcal{D}_U$. Then one has a presheaf of morphisms : \begin{align*} \underline{\text{Hom}}(x,y):(\mathcal{C} \downarrow U)^\text{op} & \longrightarrow \textbf{Set} \\ (V \stackrel{f}{\rightarrow}U) & \longmapsto \text{Hom}_{\mathcal{D}_V}(f^\ast x,f^\ast y), \end{align*} given a cleavage of $f^\ast$. Is there a similarly construction for fibred $\infty$-category?