Inclusion Criteria:

* Histologically or cytologically-confirmed R/M HNSCC that is considered incurable by local therapy.

1. * Subjects should not have had prior systemic therapy administered in the recurrent or metastatic setting. Systemic therapy which was completed more than 6 months prior to randomization if given as part of multimodal treatment for locally advanced disease is allowed.
2. * The eligible primary tumor locations are the oropharynx, oral cavity, hypopharynx, and larynx.
3. * PD-L1 expression level Combined Positive Score (CPS) ≥ 1 by immunohistochemistry (IHC) testing.
4. * Have human papilloma virus (HPV) testing result for oropharyngeal cancer defined as p16 IHC testing.
5. * Measurable disease according to RECIST 1.1 determined by the Investigator.
6. * Tumor samples (archival or fresh tumor biopsy) are required. If archival tissue is unavailable, must provide fresh tumor tissue biopsy prior to randomization.
7. * Recovery to baseline or ≤ Grade 1 severity (CTCAE v5) from adverse events (AEs) related to any prior treatments, unless AE(s) are clinically nonsignificant and/or stable on supportive therapy.
8. * Age 18 years or older on the day of consent.
9. * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1.
10. * Adequate organ and marrow function.

Exclusion Criteria:

1. * Nasopharynx, salivary gland or occult primary site (regardless of p16 status).
2. * Has disease that is suitable for local therapy administered with curative intent.
3. * Has received prior therapy with zanzalintinib, any anti-PD-1, anti-PD-L1, or anti-PD-L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (eg, CTLA-4, OX-40, CD137).
4. * Life expectancy \< 3 months.
5. * Had progressive disease within 6 months of completion of curatively intended systemic treatment for locoregionally advanced HNSCC.
6. * Radiation therapy for bone metastases within 2 weeks, any other radiation therapy within 4 weeks prior to randomization.
7. * Known brain metastases or cranial epidural disease unless adequately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks prior to randomization.
8. * Positive hepatitis B surface antigen (HBsAg) test.
9. * Positive hepatitis C virus (HCV) antibody test.
10. * Major surgery (eg, GI surgery, removal or biopsy of brain metastasis) within 8 weeks prior to randomization. Complete wound healing from major or minor surgery must have occurred at least prior to randomization.
11. * Corrected QT interval calculated by the Fridericia formula (QTcF) \> 480 ms per electrocardiogram (ECG) within 28 days before randomization.
12. * Pregnant or lactating females.
13. * Administration of a live, attenuated vaccine within 30 days before randomization.