This is a phase 2 study to investigate the efficacy and safety of DZD8586 in combination in participants with CLL/SLL.

This study consists of two parts: Part A is the safety lead-in phase, and Part B is the dose expansion phase.

Inclusion Criteria:

1. Male and female ≥ 18 years of age.
2. ECOG performance status 0-2, and life expectancy ≥ 6 months.
3. Confirmed newly diagnosis or treatment naïve CLL/SLL with indication for treatment.
4. Patients with SLL must have at least one measurable lesion.
5. Adequate bone marrow reserve and organ functions.
6. Willing to comply with contraceptive restrictions.

Exclusion Criteria:

1. Any of previous or current treatment prohibited by protocol.
2. Any unresolved > grade 1 drug-related adverse events.
3. Known or suspected Richter's transformation, or prolymphocytic leukemia.
4. CNS involvement.
5. Active infection.
6. Any of severe cardiac or pulmonary abnormalities.
7. Poorly controlled autoimmune anemia or autoimmune thrombocytopenia.
8. Poorly controlled gastrointestinal disorder, inadequate absorption of medication or other systemic diseases.
9. Prior malignancy within the past 3 years.
10. Known allergy to study drugs, any of the ingredients of the study drugs, or xanthine oxidase inhibitors or rasburicase.