Inclusion Criteria:

1. Ages 18 years old or above
2. A confirmed diagnosis of MCL according to World Health Organization (2016) criteria
3. At least one site of measurable disease not previously irradiated (defined as at least one bi-dimensionally measurable nodal lesion of greater than or equal to 1.5cm in longest dimension)
4. Life expectancy (in the opinion of the investigator) of greater than or equal to 18 weeks
5. Prior therapy with a BTK inhibitor alone or in combination and:
   1. Progression or relapse post BTK inhibitor or
   2. Failed to achieve PR following 12 weeks of BTK inhibitor therapy
6. Prior TRAEs must have recovered to Grade 1 or less with the exception of alopecia, peripheral neuropathy and lymphopenia.
7. ECOG 0-2
8. Adequate washout of prior therapies:
   1. Broad field radiation (greater than or equal to 30% of the bone marrow or whole brain radiotherapy) must be completed 14 days prior to study treatment
   2. Palliative limited field radiation must be completed 7 days prior to study treatment.
   3. Targeted agents, investigational agents, therapeutic monoclonal antibodies/antibody drug conjugates or cytotoxic chemotherapy must be completed 5 half-lives or 2 weeks (whichever is shorter) prior to study treatment (except for BTK inhibitors which may be continued until 1 day prior to planned first therapy with pirtobrutinib)
   4. Steroids (prednisolone less than or equal to 100mg daily or equivalent for up to 14 days are permitted during screening for control of lymphoma related symptoms
9. Ability to take oral medications
10. Willing and capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the ICF and in the protocol.
11. Willingness of men and women of reproductive potential to observe conventional and highly effective and acceptable birth control methods for the duration of treatment and for six months following the last dose of study treatment
12. Women of childbearing potential must have a negative serum pregnancy test within seven days of enrolment
13. Adequate coagulation, defined as aPTT and PT not greater than 1.5xULN, unless laboratory abnormality is explained by concomitant anticoagulant medication, a lupus anticoagulant, or a factor deficiency not associated with an increased bleeding risk, as determined by the investigator.
14. Adequate liver function:
    • ALT and AST less than or equal to 3X ULN, or less than or equal to 5X ULN if documented liver involvement
    • Total bilirubin less than or equal to 1.5X ULN or less than or equal to 5X ULN if documented liver involvement and/or Gilbert’s Disease
15. Adequate renal function- Creatinine clearance greater than or equal to 30mls/minute according to Cockroft-Gault formula
16. Adequate haematological parameters
    • Haemoglobin greater than or equal to 80g/L (transfusion support permitted)
    • Absolute neutrophil count greater than or equal to 1.0×10^9/L (May be G-CSF supported)
    • Platelets greater than or equal to 75 X 10^9/L. OR platelets greater than or equal to 50 X 10^9/L if documented marrow involvement or splenomegaly (must be platelet transfusion independent for 7 days prior to first dose of obinutuzumab
17. Sufficient archival tissue is available for central review or after discussion with the CPI

Exclusion Criteria:

1. Inability to comply with protocol mandated hospitalisations
2. For patients enrolling on the safety cohort, a history of allogeneic transplantation within 12 months of enrolment or ongoing chronic GVHD or immunosuppressive therapy.
3. Autologous SCT or CAR-T therapy within 6 weeks of enrolment
4. Active central nervous system involvement with MCL
5. Prior treatment with pirtobrutinib or demonstrated refractoriness to a CD20xCD3 bispecific antibody.
6. Have a known severe hypersensitivity to any of the excipients of pirtobrutinib, glofitamab, tocilizumab or obinutuzumab.
7. History of stroke or intracranial haemorrhage within six months of enrolment.
8. Live vaccination within 28 days of enrolment.
9. Major surgery or significant traumatic injury within 28 days of study treatment or the anticipation of major surgery during study treatment (surgical procedures for the diagnosis of lymphoma such as lymph node resection/ laparoscopy are allowed provided patient is considered fit for treatment as judged by investigator)
10. Significant cardiovascular disease defined as:
    1. Unstable angina or acute coronary syndrome within 2 months of registration
    2. History of myocardial infarction within 3 months prior to registration
    3. Documented LVEF by any method of = 40% during screening
    4. Grade 3 or higher NYHA functional classification system of heart failure
    5. Uncontrolled or symptomatic arrhythmias
11. Prolongation of the QT interval corrected for heart rate (QTcF) greater than 470 msec on at least 2/3 consecutive electrocardiograms (ECGs), and mean QTcF greater than 470 msec on all 3 ECGs, during Screening. QTcF is calculated using Fridericia’s Formula (QTcF): QTcF euqal to QT/(RR0.33) Correction of suspected drug-induced QTcF prolongation can be attempted at the investigator’s discretion and only if clinically safe to do so with either discontinuation of the offending drug or switching to another drug not known to be associated with QTcF prolongation. Correction for underlying bundle branch block (BBB) allowed. Patients with pacemakers are eligible if they have no history of fainting or clinically relevant arrhythmias
12. Known human immunodeficiency virus (HIV) infection
13. Known active HBV or HCV infection based on criteria below:
    1. HBV: Patients with positive HbsAg are excluded. Patients with positive hepatitis B core antibody antiHBc and negative HbsAg require negative hepatitis B PCR before enrolment and must be treated with antiviral therapy. Patients who are hepatitis B PCR positive will be excluded.
    2. HCV: If positive hepatitis C antibody, patient will need to have a negative hepatitis C RNA before enrolment. Patients who are hepatitis C RNA positive will be excluded.
14. Known active CMV infection. Unknown or negative status are eligible.
15. Pregnancy, lactation or plan to breastfeed during the study or within 6 months of the last dose of study treatment.
16. Clinically significant active malabsorption syndrome or other condition likely to affect gastrointestinal (GI) absorption of pirtobrutinib.
17. Evidence of other clinically significant uncontrolled condition(s) including but not limited to, uncontrolled systemic bacterial, viral, fungal or parasitic infection, or other clinically significant active disease process which in the opinion of the investigator and medical monitor may pose a risk for patient participation.
18. Active uncontrolled auto-immune cytopenia (e.g., AIHA, ITP) for which new therapy was introduced or existing therapy was escalated within the 4 weeks prior to study enrolment to maintain adequate blood counts, unless auto-immune cytopenias are secondary to MCL
19. Active second malignancy unless in remission and with life expectancy greater than 2 years.
20. Current treatment with strong cytochrome P450 3A4 (CYP3A4) inhibitors or inducers and/or strong P-gp inhibitors.
21. Patients requiring therapeutic anticoagulation with warfarin or another vitamin K antagonist.