Background: While tricuspid annuloplasty (TAP) is an effective treatment option for tricuspid regurgitation (TR), understanding the echocardiographic factors contributing to recurrent TR can help in developing more effective preventive measures to reduce the rate of recurrent TR after TAP. Methods: This study was designed as a prospective observational cohort study to investigate factors contributing to recurrent TR following surgical tricuspid valve (TV) repair in patients with moderate or severe functional TR caused by left heart valvular disease, with severe mitral regurgitation as the dominant pathology. The study included 66 patients who underwent preoperative two-dimensional (2D) and three-dimensional (3D) echocardiographic assessments. Patients were divided into two groups based on TAP outcomes: the effective TAP group and the recurrent TR group. Results: The analysis revealed that 3D-derived both septal–lateral diastolic and systolic tricuspid annulus (TA) diameter (odds ratio (OR) 1.77; 95% confidence interval (CI) 1.17–2.68 and OR 1.62; 95% CI 1.14–2.29, respectively), and major axis diastolic TA diameter (OR 1.59; 95% CI 1.15–2.2) had the highest OR among all echocardiographic parameters. The further univariate analysis of predefined echocardiographic values unveiled that the combined effect of heightened 3D-measured TA major axis diastolic diameter and increased right ventricle (RV) basal diameter exhibited the highest OR at 12.8 (95% CI 2.3–72.8) for a recurrent TR. Using ROC analysis, diastolic major axis (area under the curve (AUC) 0.848; cut-off 48.5 mm), septal-lateral systolic (AUC 0.840; cut-off 43.5 mm) and diastolic (AUC 0.840; cut-off 46.5 mm) TA diameter demonstrated the highest predictive value for recurrent TR from all TV parameters. Conclusions: Recurrent moderate or severe TR after TAP is associated with preoperative TA size, right atrium and RV geometry, but not with changes of RV function. The predictive capacity of 2D-assessed echocardiographic parameters was found to be lower when compared to their corresponding 3D parameters.