We explore temporal dependency graph (TDG) parsing in the clinical domain. We leverage existing annotations on the THYME dataset to semi-automatically construct a TDG corpus. Then we propose a new natural language inference (NLI) approach to TDG parsing, and evaluate it both on general domain TDGs from wikinews and the newly constructed clinical TDG corpus. We achieve competitive performance on general domain TDGs with a much simpler model than prior work. On the clinical TDGs, our method establishes the first result of TDG parsing on clinical data with 0.79/0.88 micro/macro F1.