ALPINE: Maintenance Letrozole/Abemaciclib

Inclusion Criteria: * Participants must have histologically confirmed either i) endometrioid endometrial cancer or ii) endometrial carcinosarcoma with endometrioid epithelial component. * Participants must have ER-positive disease, defined as ≥ 1 percent of tumor cell nuclei being immunoreactive by immunohistochemistry (IHC). If multiple analyses have been performed, judgment should be based on the most recent biopsy or pathology specimen analyzed in a CLIA (Clinical Laboratory Improvement Amendments)-certified laboratory. * Tumor must be TP53 wild-type as determined by immunohistochemistry (IHC) or via CLIA-certified targeted Next-Generation Sequencing (NGS); IHC assessment of p53 status is included in the NCCN guidelines of uterine neoplasms for the molecular analysis of endometrial carcinoma. * Participants must have mismatch repair proficient (MMRP) endometrial cancer as determined by immunohistochemistry (IHC) or polymerase chain reaction (PCR) or any CLIA-certified next generation sequencing assay. * No known tumor mutational burden ≥ 10 mutations/megabase (Mb). * No known RB1 mutations or two-copy RB1 deletion. * Participants must have just completed a minimum of 4 cycles and a maximum of 10 cycles of a combination of carboplatin and taxane or a combination of taxane and anti-PD-(L)1 inhibitor therapy (e.g., pembrolizumab, or dostarlimab, or durvalumab). * Participants must have had measurable stage III, measurable stage IVA, stage IVB (with or without measurable disease) or recurrent (with or without measurable disease) endometrial cancer. * Participants are permitted to have received: * a. Prior adjuvant chemotherapy (e.g., paclitaxel/carboplatin alone or as a component of concurrent chemotherapy and radiation therapy \[with or without cisplatin\]) * b. Prior radiation therapy for treatment of endometrial cancer. Prior radiation therapy may have included pelvic radiation therapy, extended field pelvic/paraaortic radiation therapy, intravaginal brachytherapy, and/or palliative radiation therapy. All radiation therapy must have been completed at least 4 weeks prior to registration. * c. Prior hormonal therapy for treatment of endometrial cancer. * Must be able to initiate study drug between 3 to 8 weeks (or 21 to 56 days) after completion of their final dose of chemotherapy and anti-PD-(L)1 blockade (if they were receiving anti-PD-(L)1 blockade). * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 (see Appendix A) * Age ≥ 18 years * Participants must have normal organ and bone marrow function within 2 weeks before starting protocol therapy as defined below: * System Laboratory Value * Hematologic * ANC ≥1.5 × 109 /L * Platelets ≥100 × 109 /L * Hemoglobin ≥8 g/dL 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. * Hepatic * Total bilirubin ≤1.5 × ULN Patients with Gilbert's syndrome with a total bilirubin ≤2.0 times ULN and direct bilirubin within normal limits are permitted. * ALT and AST ≤3 × ULN * Creatinine ≤ 1.5 × institutional ULN, OR * Creatinine clearance ≥ 60 mL/min/1.73 m2 for participants with creatinine levels above 1.5 x institutional ULN. * Abbreviations: ALT = alanine aminotransferase; ANC = absolute neutrophil count; AST = aspartate aminotransferase; ULN = upper limit of normal. * Ability to understand and the willingness to sign a written informed consent document. * Ability to swallow and retain oral medication. * Participants must be willing to release archival tissue if available. Please see section 9.1.2 and the laboratory manual for tissue requirements. Exclusion Criteria: * Participants who have received previous treatment with CDK4/6 inhibitors, including but not limited to previous abemaciclib therapy. * Any gastrointestinal dysfunctions that could interfere with the absorption of study drugs (e.g., bowel obstruction, inability to swallow tablets, malabsorption syndrome, unresolved nausea, vomiting, diarrhea CTCAE v 5.0 \> grade 1). * Patients who received chemotherapy must have recovered (Common Terminology Criteria for Adverse Events \[CTCAE\] Grade ≤1) from the acute effects of chemotherapy except for residual alopecia or Grade 2 peripheral neuropathy prior to starting study treatment. * The patient has active systemic bacterial infection (requiring intravenous \[IV\] antibiotics at time of initiating study treatment), fungal infection, or detectable viral infection (such as known human immunodeficiency virus positivity or with known active hepatitis B or C \[for example, hepatitis B surface antigen positive\]. Screening is not required for enrollment. * Major injuries or surgery within 14 days prior to start of study treatment and/or planned major surgery during the on-treatment study period. Patients who received radiotherapy must have completed and fully recovered from the acute effects of radiotherapy. A washout period of at least 14 days is required between end of radiotherapy and starting study treatment. * Other malignant disease with disease-free ≤ 3 years except: curatively treated carcinoma in situ of the cervix, basal cell carcinoma of the skin, or ductal carcinoma in situ (DCIS) of the breast or any other cancer deemed by the investigator to be at low risk for recurrence of that malignancy. * Active brain metastases (e.g., stable for \< 8 weeks, no adequate previous treatment with radiotherapy and/or surgery, symptomatic, requiring treatment with anti-convulsant therapy. Corticoid therapy is allowed if administered as stable dose for at least 1 month before starting study treatment). * Females who are pregnant or lactating. The effects of the study agents on the developing human fetus are unknown. For this reason, women of child-bearing potential must agree to use a medically approved contraceptive method during the trea