Let $C$ and $D$ be presentable stable $\infty$-categories, and let $f:C \to D$ be a continuous functor between them. Let $0$ be the trivial stable $\infty$-category. What is the colimit of the diagram

$$0 \leftarrow C \rightarrow D$$

in the $\infty$-category of presentable stable $\infty$-categories and continuous functors? For example, is it a localization of $D$?