Inclusion Criteria:

          -  Subject diagnosed with R/R AML or R/R higher risk MDS is defined as:

               -  R/R AML: Morphologically documented primary or secondary AML by the WHO criteria
                  (2016); and refractory to at least 2 cycles of induction chemotherapy/not a
                  candidate for re-induction or relapsed after achieving remission with a prior
                  therapy; and received all standard therapies including targeted therapies (unless
                  the therapy is contraindicated or intolerable) which are known to provide
                  clinical benefit in the opinion of the treating investigator; and received
                  salvage therapy or is not a candidate for salvage therapy.

               -  R/R higher risk MDS: Has MDS by the WHO criteria (2016); and either relapsed
                  after achieving remission or refractory to standard therapies, including ≥ 4
                  cycles of hypomethylating agents (unless the therapy is contraindicated or
                  intolerable); and is classified as higher risk MDS with a score of > 3.5 by
                  Revised International Prognostic Scoring System (IPSS-R) in MDS.

          -  Subject has an Eastern Cooperative Oncology Group performance status of ≤ 2.

          -  Subject must meet the following criteria as indicated on the clinical laboratory tests
             during screening period:

               -  Serum aspartate aminotransferase and alanine aminotransferase ≤ 2.5 × upper limit
                  of normal (ULN).

               -  Serum total bilirubin ≤ 1.5 × ULN.

               -  Serum creatinine ≤ 1.5 × ULN or an estimated glomerular filtration rate of > 50
                  mL/min as calculated by the Modification of Diet in Renal Disease equation.

          -  Platelets ≥ 50,000/μL at cycle 1 day 1 (C1D1) in the dose escalation cohorts only.

          -  Subject has a life expectancy of ≥ 12 weeks at the time of screening.

          -  Subjects with AML must have peripheral blood absolute blast count of < 20,000/μL at
             C1D1. Note: Blast count can be controlled by hydroxyurea during screening period.

          -  Female subject is not pregnant and at least 1 of the following conditions apply:

               -  Not a woman of childbearing potential (WOCBP).

               -  WOCBP who agrees to follow the contraceptive guidance from the time of informed
                  consent through at least 180 days after final study treatment administration.

          -  Female subject must agree not to breastfeed starting at screening and throughout the
             study period and for 180 days after the final study treatment administration.

          -  Female subject must not donate ova starting at first dose of investigational product
             (IP) and throughout the study period and for 180 days after final study treatment
             administration.

          -  Male subject with female partner(s) of childbearing potential (including breastfeeding
             partner) must agree to use contraception throughout the treatment period and for 180
             day after final study treatment administration.

          -  Male subject must not donate sperm during the treatment period and for 180 days after
             the final study treatment administration.

          -  Male subject with pregnant partner(s) must agree to remain abstinent or use a condom
             for the duration of the pregnancy throughout the study period and for 180 days after
             final study treatment administration.

          -  Subject agrees not to participate in another interventional study while receiving
             study treatment in the present study.

        Exclusion Criteria:

          -  Subject was diagnosed with acute promyelocytic leukemia.

          -  Subject has breakpoint cluster region-Abelson-positive leukemia (BCR-ABL).

          -  Subject has persistent non-hematological toxicities of ≥ grade 2 (National Cancer
             Institute's Common Terminology Criteria for Adverse Events [NCI-CTCAE], version 5.0),
             with symptoms and objective findings from prior AML or MDS treatment (including
             chemotherapy, kinase inhibitors, immunotherapy, experimental agents, radiation or
             surgery).

          -  Subject has received any of the following therapies:

               -  Systemic immunomodulators or immunosuppressive drugs including steroids ≤ 28 days
                  prior to C1D1 (steroids can be used if not intended for treatment of AML or MDS;
                  steroids for AML/MDS related symptoms can be used at low doses [less than 10
                  mg/day dexamethasone]).

               -  Cytotoxic agents (except hydroxyurea given for controlling blast cells) ≤ 28 days
                  prior to C1D1.

               -  Investigational products for the treatment of AML or MDS within 5 half-lives
                  prior to screening visit.

               -  Hematopoietic stem cell transplant (HSCT).

               -  Radiation therapy ≤ 28 days prior to C1D1.

          -  Subject has clinically active nervous system leukemia.

          -  Subject has active or prior documented autoimmune or inflammatory disorders requiring
             systemic treatment.

          -  Subject has ongoing, untreated malignancy with the exception of the following:

               -  Subjects with treated non-melanoma skin cancer, in situ carcinoma or cervical
                  intraepithelial neoplasia, regardless of the disease-free duration, are eligible
                  for this study if definitive treatment for the condition has been completed.

               -  Subjects with organ-confined prostate cancer with no evidence of recurrent or
                  progressive disease are eligible if hormonal therapy has been initiated or the
                  malignancy has been surgically removed or treated with definitive radiotherapy.

          -  Subject with left ventricular ejection fraction of < 45% on echocardiogram or
             multigated acquisition scan (MUGA) performed within 28 days of screening.

          -  Subject has laboratory abnormalities, or clinical evidence of disseminated
             intravascular coagulation, or ongoing history of coagulation disorder manifested by
             bleeding or clotting.

          -  Subject has an active uncontrolled infection.

          -  Subject is known to have human immunodeficiency virus infection.

          -  Subject has active hepatitis B or C or other active hepatic disorder.

          -  Subject has any condition which makes the subject unsuitable for study participation.

          -  Subject has a known or suspected hypersensitivity to bovine-derived protein or has
             suspected hypersensitivity to any ingredients of ASP7517.

          -  Subject is eligible for HSCT.