Pivotal Trial to Evaluate TraNsvenous TrIcuspid Valve ReplacemenT With LuX-Valve Plus System (The TRINITY Pivotal Trial)

Inclusion Criteria: For the randomized study: 1. Subject is at least 21 years of age at time of consent. 2. Subject (or legal guardian) understands trial requirements and treatment procedures and is able to provide written informed consent. 3. Severe or greater TR as assessed on transthoracic echocardiography by core lab. 4. New York Heart Association (NYHA) Class II-IV. 5. On optimal medical therapy (OMT) for TR at the time of baseline assessment per site Heart Team. OMT includes stable oral diuretic medications unless patient has a documented history of intolerance. 6. The site Heart Team concurs that the patient is a good candidate for transcatheter tricuspid valve replacement and suitable for LuX-Valve Plus system by core lab. 7. The commercial sponsor for EVOQUE deems that the patient is a good candidate for EVOQUE valve (control arm). For single arm cohort ("Not Suitable for Conventional TTVI") 1. Meets all criteria 1-6 above 2. The EVOQUE commercial sponsor deems the anatomy unsuitable for EVOQUE tricuspid valve replacement, or the annular perimeter is smaller or greaterthan EVOQUE commercial Instructions for Use (IFU), as determined by the clinical site 3. Two independent Structural Cardiologists determine the patient "Not Suitable" for Triluminate edge to edge repair Exclusion Criteria: 1. Left ventricular ejection fraction (LVEF) \<35%. 2. Pulmonary arterial systolic pressure (PASP) \>60 mmHg by echo Doppler (unless right heart catheterization \[RHC\] demonstrates PASP ≤60mmHg); in case RHC is performed, PASP \>2/3 systemic BP with PVR \>5 Wood units after vasodilator challenge, in the absence of symptomatic hypotension or systolic BP \<90 mmHg. 3. Evidence of intracardiac mass, thrombus, or vegetation. 4. Ebstein Anomaly or congenital right ventricular dysplasia. 5. Surgical or interventional correction is indicated for other concomitant valvular diseases (subjects with concomitant valvular disease may treat their respective valve first and wait 2 months before being reassessed for the trial). 6. Subjects with valve prostheses implanted in the tricuspid valve. 7. Pre-existing prosthetic valve(s) (other than tricuspid ones) with clinically significant prosthetic dysfunction. 8. Active infection, infective endocarditis or sepsis within 3 months, or infections requiring antibiotics treatment within two weeks prior to planned procedure. 9. Untreated clinically significant coronary artery disease requiring revascularization. 10. Acute myocardial infarction or unstable ischemia-related angina within 30 days prior to the planned procedure. 11. Any percutaneous coronary, intracardiac or carotid intervention within 30 days prior to the planned procedure. 12. Cerebrovascular stroke (ischemic or bleeding) within 3 months prior to enrollment. 13. Active peptic ulcer or active gastrointestinal bleeding within 3 months prior to enrollment. 14. Blood dyscrasias as defined: leukopenia (WBC \<1000 mm3), thrombocytopenia (platelet count \<50,000 cells/mm3), history of bleeding diathesis, or coagulopathy. 15. Inability to tolerate anticoagulation or antiplatelet therapy. 16. Renal insufficiency (eGFR\< 30ml/min \[per the CKD-EPI formula\] and/or renal replacement therapy). 17. Patients with hepatic insufficiency or cirrhosis with Child-Pugh score class C 18. Pregnancy or intent to become pregnant prior to completion of all protocol follow-up requirements. 19. Severe Chronic Obstructive Pulmonary Disease requiring steroids or requiring continuous home oxygen. 20. Untreatable hypersensitivity or contraindication to any of the following: all antiplatelets, all anticoagulants, nitinol alloys (nickel and titanium), bovine tissue, glutaraldehyde, or contrast media. 21. Estimated life expectancy \<12 months. 22. Subjects currently participating in another clinical trial of an investigational drug or device that has not yet completed its primary endpoint. 23. Subjects with current history of illicit drug use. 24. Any other condition making it unlikely the patient will be able to complete all protocol procedure and follow-ups determined by the investigator.