This study will treat patients with CLL/SLL whose disease comes back or is not responding to prior therapy, or if they can not bear side effects of the prior treatment. This study will assess the anti-tumor activity of DZD8586 as monotherapy. It will help to understand what type of side effects may occur with the drug treatment. It will also measure the levels of drug in the body.

Inclusion Criteria:

Participants who meet all the following criteria:

1. Male and female ≥ 18 years of age.
2. ECOG performance status 0-2.
3. Confirmed diagnosis of CLL/SLL with indication for treatment.
4. Adequate bone marrow reserve and organ system functions.
5. Willing to comply with contraceptive restrictions.

Exclusion Criteria:

Participants who meet any of the following criteria:

1. CNS involvement or Richter transformation.
2. Stem cell transplantation, cell therapy, or gene therapy within 90 days. Approved small molecule therapy within 5 half-lives, monoclonal antibodies and antibody-drug conjugates within 28 days.
3. Major surgery or significant traumatic injury within 4 weeks. Live attenuated vaccines or viral vector vaccines within 4 weeks.
4. Take vitamin K antagonists or take more than 2 anticoagulants or antiplatelet drugs at the same time. Take proton pump inhibitors or strong CYP3A inhibitors or inducers.
5. Active infection.
6. Clinically significant cardiac disorders or abnormalities. History of thrombotic diseases, stroke or intracranial hemorrhage within 6 months.
7. Nausea and vomiting not controlled or chronic gastrointestinal diseases, unable to swallow the formulated product or previous bowel resection that would preclude adequate absorption.
8. Another malignancy within 2 years prior to enrollment with the exception of adequately treated in-situ carcinoma of the cervix, uterus, basal or squamous cell carcinoma or non-melanomatous skin cancer.
9. Women who are breast feeding.
10. History of hypersensitivity to active or inactive excipients of DZD8586 or drugs with a similar chemical structure or class.