Hypoplastic Left Heart Syndrome (HLHS) is a congenital heart defect that requires a three-stage surgical palliation to create a single ventricle system in the right side of the heart. Of patients undergoing this cardiac palliation series, 25% will develop tricuspid regurgitation (TR), which is associated with an increased mortality risk. Valvular regurgitation in this population has been extensively studied to understand indicators and mechanisms of comorbidity. In this article, we review the current state of research on TR in HLHS, including identified valvular anomalies and geometric properties as the main reasons for the poor prognosis. After this review, we present some suggestions for future TR-related studies to answer the central question: What are the predictors of TR onset during the three palliation stages? These studies involve (i) the use of engineering-based metrics to evaluate valve leaflet strains and predict tissue material properties, (ii) perform multivariate analyses to identify TR predictors, and (iii) develop predictive models, particularly using longitudinally tracked patient cohorts to foretell patient-specific trajectories. Regarded together, these ongoing and future efforts will result in the development of innovative tools that can aid in surgical timing decisions, in prophylactic surgical valve repair, and in the refinement of current intervention techniques.