In this article, we address a two-stage scheduling problem that requires coordination between clinical and surgical appointments for specialized surgeries. First, patients have a clinical appointment with a surgeon to determine whether they are an appropriate candidate for the surgical procedure. Subsequently, if the decision to pursue the surgery is made the patient undergoes the procedure on a later date. However, the scheduling process aims to book both the clinical and surgical appointments for a patient at the time of the initial appointment request. Two sources of uncertainty make this scheduling process challenging: (i) the patient may or may not need surgery after the clinical appointment and (ii) the surgery duration for each patient and procedure is unknown. We present a Distributionally Robust Optimization (DRO) approach for coordinating clinical and surgical appointments under these uncertainties. A case study of the Transcatheter Aortic Valve Replacement procedure at Mayo Clinic, Rochester, MN is presented. Numerical results include comparisons with the current practice and four heuristic scheduling policies from the literature. Results show that the DRO-based scheduling policies lead to lower total surgeon idle-time and overtime per day. The proposed policies also restrict the under and over utilization of clinical capacity.