The purpose of the study is to determine the activity and safety of ACR-368 (prexasertib) in combination with gemcitabine in participants with Head and Neck Squamous Cell Carcinoma (HNSCC). Participants will receive the study drugs ACR-368 and a low dose of gemcitabine once every 2 weeks in 4-week cycles and will continue on treatment unless the disease deteriorates.

Inclusion Criteria:

• Patient (or a legally authorized representative) must understand and voluntarily sign informed consent prior to any study-related assessments/procedures being conducted.
• Must be able and willing to comply with the study visit schedule and protocol requirements.
• Must have sufficient archived tumor tissue available for p16 immunohistochemistry (IHC) staining if the status is unknown. HPV status determined by HPV DNA sequencing, HPV DNA/RNA in situ hybridization, or equivalent assays using tumor tissue or cell free HPV DNA testing or equivalent using blood-based assays are also acceptable. If there is a discrepancy between p16 IHC and HPV detection assay results, HPV detection assay result will be used.
• Must have sufficient archived tumor tissue available for OncoSignature determination. The tumor tissue must be less than 3 months old from the enrollment date. There should not be any intervening systemic therapy from the date of tumor tissue collection. If not, patient must agree to a fresh tumor biopsy before starting the treatments.
• Must agree to a biopsy after the lead-in LDG infusion and at the time of disease progression (or end of treatment if applicable).
• Must have R/M HNSCC including oral cavity, oropharynx, larynx, and hypopharynx. Patients with p16-positive or HPV-positive unknown primary of head and neck are eligible.
• Must have been treated with one prior line of PD-1/PD-L1 inhibitor with/without chemotherapy. Patients who are immunotherapy ineligible due to history of autoimmune disease or steroid requirement (prednisone >10mg per day or equivalent) are allowed to enroll without the one prior line of PD-1/PD-L1 inhibitor with/without chemotherapy. There is no limitation on the number of prior therapies received in the R/M setting.
• Must have at least one measurable lesion as defined by RECIST v1.1.
• Must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1.
• Must meet the laboratory criteria outlined in the protocol. Blood transfusion and/or blood product support are allowed.
• Patients of childbearing potential and patients whose sexual partners are of childbearing potential must be willing to practice an approved method of highly effective birth control with their partners starting at the time of informed consent and for 1 year after the completion of the study treatment regimen.

Exclusion Criteria:

• Patients should not have any prior systemic therapy for 4 weeks from the time of the study treatment.
• Patients should not have any palliative radiation therapy for 2 weeks from the time of the study treatment. Palliative radiation therapy is permitted during the study treatment if it does not involve target lesions.
• Patients with prior therapy-related toxicities Grade >1 per National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) Version 5.0; except for dysphagia, alopecia, or vitiligo. Immunotherapy-related endocrinopathies stable for at least 1 month, and controlled with hormonal replacement, are not excluded. Grade 2 neuropathy stable for at least 2 weeks and controlled with supportive care medications are not excluded.
• Patients with symptomatic and/or untreated brain metastases (of any size and any number). Patients with definitively treated brain metastases may be eligible, must be stable for at least 2 weeks and must be asymptomatic with or without prednisone <10mg (or equivalent).
• Patients who have a left ventricular ejection fraction (LVEF) < 45% or who are New York Heart Association (NYHA) Class 2 or higher.
• Patients with cardiovascular disease defined as: A) Uncontrolled hypertension defined as blood pressure > 160/90 mmHg at Screening confirmed by repeat (medication permitted). B) History of torsades de pointes, significant Screening electrocardiogram (ECG) abnormalities, including ventricular rhythm disturbances, unstable cardiac arrhythmia requiring medication, pathologic symptomatic bradycardia, left bundle branch block, second degree atrioventricular (AV) block type II, third degree AV block, Grade ≥ 2 bradycardia, uncorrected hypokalemia not amenable to correction, congenital long QT syndrome, prolonged QT interval due to medications, corrected QT (QTc) > 450 msec (for men) or > 470 msec (for women). C) Symptomatic heart failure (per New York Heart Association guidelines; (Caraballo, 2019), unstable angina, myocardial infarction, severe cardiovascular disease (ejection fraction < 20%, transient ischemic attack, or cerebrovascular accident within 6 months of Day 1).
• Patients who have had another primary malignancy within the previous 3 years (except for those who do not require treatment or have been curatively treated >1 year ago, and in the judgment of the Investigator, do not pose a significant risk of recurrence; including, but not limited to, non-melanoma skin cancer, ductal carcinoma in situ [DCIS] or lobular carcinoma in situ [LCIS], or prostate cancer Gleason score ≤6.).
• Patients who are of the following protected classes will be excluded: Pregnant, parturient, or breastfeeding women. Persons who are hospitalized without consent or those deprived of liberty because of a judiciary or administrative decision. Patients with a legal protection measure or a person who cannot express his/her consent and for whom a legally authorized representative is not available.
• Patients in emergency situations who cannot consent to the study and for whom a legally authorized representative is not available.