Evaluation of ABEMACICLIB Monotherapy in Patients With Locally Advanced/Metastatic Head and Neck Cancer After Failure of Platinum and Cetuximab or Anti-EGFR-based Therapy and Harboring an Homozygous Deletion of CDKN2A, and/or an Amplification of CCND1 and/or of CDK6

Inclusion Criteria: * I1. Male or female patients aged ≥ 18 years at time of inform consent signature * I2. Histologically proven metastatic or locally advanced HNSCC (oropharynx, oral cavity, hypopharynx and larynx). Patients with cancer of nasopharynx (i.e. cavum cancer) are not eligible * I3. Availability of a representative formalin-fixed paraffin-embedded (FFPE) primary and/or metastatic tumor tissue with an associated pathology report for molecular pre-screening: either an archival tumor block or a dedicated freshly collected tumor biopsy. * I4. Documented CDKN2A homozygous deletion and/or CCND1 amplification and/or CDK6 and/or CDK4 amplification and no deletion/losses more than single copy of RB1 by copy number data before C1D1. Note: This molecular pre-screening will be centralized at at the CGH platform of Centre Léon Bérard (CLB). Note: This molecular pre-screening will be centralized at the CGH platform of Centre Léon Bérard (CLB). Note: This molecular pre-screening can be performed for patient without documented disease progression (PD) but study drug treatment cannot be initiated until confirmed radiological PD. * I5. HPV negative tumor status must be documented before C1D1. Note: This analysis will be centralized and performed by translational Biopathology platform of CLB during molecular pre-screening by IHC for p16. * I6. Documented radiological progression or relapse after at least platin and cetuximab or anti-EGFR-based chemotherapy (combination or sequential treatment) and other standard treatment available at time of C1D1.. * I7. At least one measurable lesion by CT-scan as per RECIST 1.1. * I8. At least one biopsiable tumor lesion before C1D1 i.e. at least one lesion with a diameter of at least 10 mm, visible by medical imaging and accessible to percutaneous sampling. * I9. Eastern Cooperative Oncology Group (ECOG) performance status: 0 or 1. * I10. Life expectancy \> 12 weeks. * I11. Patients must be able to swallow capsules. * I12. Adequate organ and bone marrow function as defined by the following tests (to be checked using medical records and then carried out within 7 days prior C1D1): * Bone marrow : * Absolute neutrophil count \>= 1.0 x 109/L * Platelet count \> 100 x 109/L * Hemoglobin value \>= 9 g/dL Note : Patients may receive erythrocyte transfusions to achieve this hemoglobin level at the discretion of the investigator. Initial treatment must not begin earlier than the day after the erythrocyte transfusion. * Renal function * Calculated creatinine clearance by MDRD or CDK-EPI \> 50mL/min/1.73m2 * Liver function * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3 x ULN (or \< 5.0 x ULN if liver metastases are present) * Total serum bilirubin ≤ 1.5 x ULN (except for patients with Gilbert disease for whom a total serum bilirubin ≤ 3mg/dL is acceptable). * I13. Women of childbearing potential (entering the study after a confirmed menstrual period and who have a negative pregnancy test within 7 days before C1D1) must agree to use two methods of medically acceptable forms of contraception from the date of negative pregnancy test up to 3 months after the last study drug intake. * I14. Fertile males must use a highly effective contraception during dosing period and through 3 months after final dose of study drug. * I15. Patient should be able and willing to comply with study visits and procedures as per protocol. * I16. Patient should understand, sign, and date the written voluntary informed consent form at the screening visit prior to any protocol-specific procedures performed. * I17. Patients must be covered by a medical insurance. Exclusion Criteria: * NI1. Cancer disease considered curable with surgery or radiotherapy. * NI2. Patient with a concurrent malignancy or has a malignancy within 3 years of study enrollment (with the exception of adequately treated basal or squamous cell carcinoma or non-melanomatous skin cancer). * NI3. Patient with impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of abemaciclib (e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection). * NI4. Patient has other concurrent severe and/or uncontrolled medical condition that would, in the investigator's judgment contraindicate her participation in the clinical study (for example, history of major surgical resection involving the stomach or small bowel, or preexisting Crohn's disease or ulcerative colitis). * NI5. Persisting significant toxicities related to prior treatments i.e. ≥ Grade 2 AE according to CTCAE V5.0 except alopecia (any grade), grade 2 peripheral neuropathy and biological values as defined in inclusion criteria. * NI6. Hypersensitivity to the active substance or excipient of study drug. * NI7. Have received prior treatment with any CDK4/6 inhibitor (or participated in any CDK4/6 inhibitor clinical trial for which treatment assignment is still blinded). * NI8. Patient has received treatment with a drug that has not received regulatory approval for any indication within : * 14 days of C1D1 for non myelosuppressive agent or * 21 days of C1D1 for a myelosuppressive agent. * NI9. Patient has had major surgery and/or radiotherapy within 14 days prior to C1D1. * NI10. Patient has received within 28 days prior to C1D1 yellow fever vaccine. * NI11. Patient has a personal history within the last 12 months prior to C1D1 of any of the following conditions: syncope of cardiovascular etiology, ventricular tachycardia, ventricular fibrillation, or sudden cardiac arrest. * NI12. Patient needs for the following concomitant medications/interventions not permitted during the study treatment period: * Any investigational anticancer therapy other than the study drug. * Any concurrent chemotherapy, radiotherapy (except palliative radiotherapy after discussion with the Sponsor), immunotherapy, biologic or hormonal therapy for cancer treatment. Concurrent use of hormones for non-cancer-related conditions (e.g., insulin for diabetes and hormone replacement therapy) is acceptable. * Major surgery. * Strong and moderate inducers and inhibitors of CYP3A (for example grapefruit or grapefruit juice, phenytoin and carbamazepine). * Enzyme-Inducing Anti-Epileptic Drugs (EIAED). * NI13. Patient has received an autologous or allogeneic stem-cell transplant. * NI14. Patient has an active systemic fungal and/or known viral infection (for example, human immunodeficiency virus antibodies, hepatitis B surface antigen, or hepatitis C antibodies). * NI15. Pregnant or breast-feeding female patients. * NI16. Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Patients with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to C1D1and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 28 days prior to C1D1. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability