Inclusion Criteria:

1. Males or females aged ≥ 18 years.
2. a) AML/MDS with blasts \> 10% in subjects who have had an inadequate response or progression to venetoclax combinations with either HMA or low dose Ara-C or similar venetoclax combinations. or b. CLL in subjects who have received at least 2 lines of therapy, including venetoclax and a BTK inhibitor, who require therapy as per iwCLL criteria.
3. Any prior therapy must have been completed at least 2 weeks prior to enrollment on this protocol, and the participant must have recovered to eligibility levels from prior toxicity
4. Hydroxyurea may be used for the first 14 days of Cycle 1 for peripheral blast control. Valproic acid not being used for seizure control should be stopped 72 hours before starting treatment with fadraciclib.
5. Any prior therapy with decitabine or azacitidine must have been completed at least 3 weeks prior to enrollment on this protocol.
6. Subjects who relapsed post-autologous or post-allogeneic transplant are eligible. Post-transplant subjects must be without active fungal disease or significant acute graft-versus-host disease.
7. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
8. Women of childbearing potential (WOCBP) must have a negative pregnancy test (urine or serum) within 7 days prior to starting the study drug. Both males and females must agree to use effective birth control during the study (prior to receiving the first dose and for 6 months after the last dose) if conception is possible during this interval.
9. Subjects must be able to swallow and retain orally administered medication and not have any clinically significant GI abnormalities that may alter the absorption, such as malabsorption syndrome or major resection of the stomach or bowels.
10. Subjects must be able to agree to and sign the informed consent and to comply with the protocol.

Exclusion Criteria:

1. Subjects with known active leptomeningeal involvement by AML.
2. Subjects who have not received vaccines for SARS-COV-2 within the last 3 months and have suspected signs and symptoms of COVID-19 or a recent history (within 14 days) of contact with any COVID-19 positive subject/isolation/quarantine or subjects with confirmed COVID-19.
3. Subjects with a history of another primary malignancy, other than:

1. Carcinomas in situ, e.g., breast, cervix, and prostate
2. Locally excised non-melanoma skin cancer
3. No evidence of disease from another primary cancer for 2 or more years and has not taken any anticancer treatment in 2 years.
4. Any other clinically significant acute or chronic medical or psychiatric condition or any laboratory abnormality that may increase the risk associated with study drug administration or may interfere with the interpretation of study results.
5. Diseases that significantly affect GI absorption of fadraciclib.
6. Subjects who have impaired cardiac function or clinically significant cardiac disease.
7. Presence of active chronic inflammatory bowel disease (ulcerative colitis, Crohn's disease) or GI perforation within 6 months of enrollment.
8. Presence of an active infection requiring IV antibiotics.
9. Presence of known history of human immunodeficiency virus-1/2 with uncontrolled viral load and on medications that may interfere with metabolism.
10. Presence of active hepatitis B virus (HBV) or hepatitis C virus (HCV).
11. Subject has received systemic anticancer therapy (including investigational therapy), radiotherapy, or immunotherapy \< 14 days or 5 half-lives (whichever is shorter) prior to administration of Dose 1 of study drug on Day 1 or have not recovered from the side effects of such therapy.
12. Major surgery/surgical therapy for any cause within 4 weeks of the first dose.