• Written informed consent and HIPAA authorization for release of personal health information prior to registration. NOTE: HIPAA authorization may be included in the informed consent or obtained separately.

• Age ≥ 18 years at the time of consent.

• ECOG Performance Status of 0, 1, or 2 within 28 days prior to registration

• Life expectancy of 6 months or greater as determined by the site investigator.

• Subjects with histologically or cytologically confirmed squamous non-small cell lung cancer (sqNSCLC).

• Subjects with stage IV NSCLC as defined by American Joint Committee on Cancer (AJCC) 8th Edition who have not received prior therapy for stage IV NSCLC. Patients with locally advanced or recurrent disease who are candidates for first-line induction systemic therapies for stage IV NSCLC are also allowed.

• • Only patients with disease control, defined as complete response (CR), partial response (PR), or stable disease (SD) to induction therapy will be allowed to receive maintenance cabozantinib plus pembrolizumab arm of trial. Patients who have progression of disease (POD) following induction therapy will proceed to second-line therapy of local clinician's choice. Only those patients who proceed to maintenance cabozantinib and pembrolizumab therapy will be evaluable for primary and secondary objectives.

• Subjects whose tumors have been tested for PD-L1 expression.

• Demonstrate adequate organ function as defined below. All screening labs to be obtained within 14 days prior to registration.

• System Laboratory Value Hematological. White blood cell (WBC) ≥ 2.5K/uL Absolute Neutrophil Count (ANC) ≥ 1,500/uL without the support of Filgrastim or ≥ 1,000/L in subjects with constitutional neutropenia Hemoglobin (Hgb) ≥ 9 g/dL Platelets (Plt) ≥ 100,000/µL without transfusion. Renal Serum creatinine Calculated creatinine clearance1 ≤ 1.5 mg/dL

• ≥ 40 mL/min; for subjects with serum creatinine \> 1.5 mg/dL Urine protein/creatinine ratio (UPCR) ≤ 1 mg/mg (≤ 113.2 mg/mmol), or 24-h urine protein ≤ 1 g Hepatic Total Bilirubin2 OR Direct Bilirubin ≤ 1.5 × upper limit of normal (ULN) or ≤ 3 × ULN for subjects with Gilbert's disease

• ≤ ULN for subjects with total bilirubin levels \> 1.5 x ULN Aspartate aminotransferase (AST) ≤ 3 × ULN or ≤ 5 x ULN for subjects with known hepatic metastasis Alanine aminotransferase (ALT) ≤ 3 × ULN or ≤ 5 x ULN for subjects with known hepatic metastasis Alkaline phosphatase (ALP) ≤ 3 × ULN or ≤ 5 x ULN with documented bone metastases.

• Serum albumin ≥ 2.8 g/dl Coagulation International Normalized Ratio (INR)

⁃ 1.3 × ULN; For subjects receiving warfarin or LMWH, the subjects must, in the site investigator's opinion, be clinically stable with no evidence of active bleeding while receiving anticoagulant therapy. The INR for these subjects may exceed 1.3 × ULN if that is the goal of anticoagulant therapy.

‣ 1 Cockcroft-Gault formula will be used to calculate creatinine clearance (See SPM) 2 Except in patients with Gilbert's syndrome who must have a total bilirubin less than 3.0 mg/dl.

• Recovery to baseline or ≤ Grade 1 CTCAE v5.0 from toxicities related to any prior treatments, unless AE(s) are clinically nonsignificant and/or stable on supportive therapy.

⁃ Sexually active fertile subjects and their partners must agree to use medically accepted methods of contraception (e.g., barrier methods, including male condom, female condom, or diaphragm with spermicidal gel) during the course of the study and for 4 months after the last dose of cabozantinib and 4 months after the last dose of pembrolizumab.

⁃ Females of childbearing potential must have a negative serum pregnancy test within 3 days prior to registration. Female subjects of childbearing potential must not be pregnant at screening. Female subjects are considered to be of childbearing potential unless one of the following criteria is met: documented permanent sterilization (hysterectomy, bilateral salpingectomy, or bilateral oophorectomy) or documented postmenopausal status (defined as 12 months of amenorrhea in a woman \> 45 years-of-age in the absence of other biological or physiological causes. In addition, females \< 55 years-of-age must have a serum follicle stimulating (FSH) level \> 40 mIU/mL to confirm menopause). Note: Documentation may include review of medical records, medical examinations, or medical history interview by study site.

⁃ As determined by the enrolling physician or protocol designee, subjects should be capable of understanding and complying with the protocol requirements and must have signed the informed consent document.

⁃ Willingness and ability to comply with scheduled visits, treatment plans, laboratory tests, and other study procedures.