Combination of PD-1 Monoclonal Antibody and HPV Vaccine in Patients With Cervical Cancer

Inclusion Criteria: 1. Patients must have persistent, recurrent or metastatic squamous cell carcinoma, adenosquamous carcinoma or adenocarcinoma of the cervix with documented disease progression (disease not amendable to curative therapy) 2. All patents must have measurable disease as defined by RECIST 1.1; measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded); each lesion must be \>= 10 mm when measured by computed tomography (CT), magnetic resonance imaging (MRI) or caliper measurement by clinical exam;lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI 3. Patients must have at least one "target" lesion" to be used to assess response on this protocol as defined by RECIST 1.1; tumors within a previously irradiated field will be designated as "non-target" lesions unless progression is documented or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy 4. In the state of HPV infection 5. Appropriate for study entry based on the following diagnostic workup: * History/physical examination within 28 days prior to registration * Imaging of target lesion(s) within 28 days prior to registration * Further protocol-specific assessments: * Recovery from adverse effects of recent surgery, radiotherapy or chemotherapy * Any other prior therapy directed at the malignant tumor including chemotherapy, biologic/targeted agents and immunologic agents must be discontinued at least three weeks prior to registration Investigation agents must be discontinued for at least 30 days prior to registration * Any prior radiation therapy must be completed at least 4 weeks prior to registration * At least 4 weeks must have elapsed since any major surgery prior to registration 6. Patients must have had one prior systemic chemotherapeutic regimen for management of persistent, recurrent or metastatic carcinoma of the cervix (e.g.; paclitaxel/cisplatin, paclitaxel/cisplatin/bevacizumab); chemotherapy administered concurrent with primary radiation (e.g.; weekly cisplatin) is not counted as a systemic chemotherapy regimen; adjuvant chemotherapy given following the completion of radiation therapy (or concurrent chemotherapy and radiation therapy) is not counted as a systemic chemotherapy regimen (e.g.; paclitaxel and carboplatin for up to 4 cycles); NOTE: patients who have received more than one prior regimen are NOT eligible 7. Have a performance status of 0 or 1 on the ECOG Performance Scale 8. Absolute neutrophil count (ANC) \>= 1,500/ul 9. Platelets \>= 100,000/ul 10. Creatinine =\< 1.5 x institutional upper limit of normal (ULN) or creatinine clearance (CrCl) \>= 40 mL/min using Cockcroft-Gault formula 11. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x ULN Exclusion Criteria: 1. Has disease which is amenable to radical treatment with surgery or radiation or a combination of treatments. 2. Is currently participating in or has participated in a study of an investigational agent or using an investigational device within 4 weeks of the first dose of treatment. 3. Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. 4. Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent. 5. Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent. * Note: Subjects with ≤ Grade 2 neuropathy are an exception to this criterion and may qualify for the study. * Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. 6. Has a known additional malignancy that is progressing or requires active treatment. 7. Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment. 8. Has an active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents. Subjects with vitiligo or resolved childhood asthma/atopy would be an exception to this rule. Subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study. Subjects with hypothyroidism stable on hormone replacement or Sjorgen's syndrome will not be excluded from the study. 9. Has an active infection requiring systemic therapy. 10. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. 11. Has known hypersensitivity to Sintilimab or its formulation 12. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 13. Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. 14. Has received prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-Cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways). 15. Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). 16. Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). 17. History of serotonergic syndrome.