Key Inclusion Criteria:  Participants eligible for inclusion in this study must meet all of the following criteria:  Written informed consent must be obtained before any assessment is performed. Male or female participants ≥18 years of age.  Participants meeting one of the following CV category:  •Very high risk participants with the following: A. Documented Atherosclerotic Cardiovascular Disease (ASCVD) i) Acute Coronary Syndrome: Unstable angina or myocardial infarction ii) Stable angina iii) Unequivocally documented ASCVD upon prior imaging v) Stroke and Transient Ischaemic Attack (TIA) vi) Peripheral Artery Disease (PAD) B. Diabetes mellitus (DM) with target organ damage (defined as microalbuminuria, retinopathy, or neuropathy), or at least ≥ 3 major risk factors, or early onset of Type 1 DM of long duration (> 20 years) C. A calculated SCORE2 ≥ 7.5% for age < 50 years; SCORE2 ≥ 10% for age 50-69 years; SCORE2-OP ≥ 15% for age ≥ 70 years to estimate 10-year risk of fatal and non-fatal CVD D. Pre-existing diagnosis of heterozygous familial hypercholesterolemia (HeFH) with ASCVD or with another major risk factor.  •High risk participants with the following: A. Markedly elevated single risk factors, in particular total cholesterol > 8mmol/L (> 310 mg/dL), LDL-C > 4.9 mmol/dL (> 190 mg/dL), or blood pressure ≥ 180/110 mmHg B. Pre-existing diagnosis of HeFH without other major risk factors C. DM without target organ damage (defined as microalbuminuria, retinopathy, or neuropathy), with DM duration ≥ 10 years or other additional risk factor D. Moderate chronic kidney disease (eGFR 30-59 mL/min/1.73m2) E. A calculated SCORE2 2.5 to <7.5% for age under 50 years; SCORE2 5 to <10% for age 50-69 years; SCORE2-OP 7.5 to <15% for age ≥70 years to estimate 10-year risk of fatal and non-fatal CVD as defined by the cardiovascular risk categories in the 2019 ESC/EAS guideline (Mach et al 2020)  LDL-C levels:  in participants with very high cardiovascular risk: serum LDL-C ≥1.4 in participants with high cardiovascular risk: serum LDL-C ≥1.8 mmol/l (≥70 mg/dL) Participant on a stable dose of a statin for ≥ 30 days. Up to 20% of participants can be on a stable dose (for ≥ 30 days) of another LLT on top of statin such as a cholesterol absorbing inhibitor or a bile acid sequestrant, or alternatively, an adenosine triphosphate citrate lyase (ACL) inhibitor, as indicated.  Fasting triglyceride < 400 mg/dL (< 4.52 mmol/L).  At Baseline:  Fasting triglyceride < 400 mg/dL (< 4.52 mmol/L).  Before randomization, despite being treated with the individual MTD of a statin for ≥ 30 days and, if applicable, with another LLT on top of statin (stable for ≥ 30 days),  in participants with very high cardiovascular risk: serum LDL-C ≥ 1.4mmol/L (≥ 55mg/dL). in participants with high cardiovascular risk: serum LDL-C ≥ 1.8mmol/L (≥ 70mg/dL).  Key Exclusion Criteria: Participants meeting any of the following criteria are not eligible for inclusion in this study.  Severe concomitant non-CV disease that is expected to reduce life expectancy to less than 2 years at screening or baseline visit. Participants on more than one other lipid-lowering drug on top of statin at screening visit. Pre-existing diagnosis of homozygous familial hypercholesterolemia at screening or baseline visit. Secondary hypercholesterolemia, e.g. hypothyroidism or nephrotic syndrome at screening or baseline visit. Previous (within 90 days of screening), current or planned treatment with a monoclonal antibody (mAb) directed towards PCSK9 (e.g. evolocumab, alirocumab) at screening or baseline visit. Previous exposure to inclisiran or any other non-mAb PCSK9 targeted therapy, either as an investigational or marketed drug within 2 years prior to screening or baseline visit. Previous, current or planned treatment with LDL-apheresis at screening or baseline visit. Participants with known intolerance to rosuvastatin at screening or baseline visit. History of hypersensitivity to any of the study treatments, inclisiran or rosuvastatin, or its excipients or to drugs of similar chemical classes at screening or baseline visit. Participants taking gemfibrozil at screening or baseline visit. Liver and CK: (a) Active liver disease defined as any current infectious, neoplastic, or metabolic pathology of the liver or (b) unexplained alanine aminotransferase (ALT), aspartate aminotransferase (AST) elevation >3x ULN, or total bilirubin elevation > 2x ULN (except for participants with Gilbert's syndrome), or (c) creatine kinase (CK) >5x ULN at screening or baseline visit. Participant with severe renal impairment defined by eGFR <30 mL/min/1.73m2 as calculated by the Modification in Diet in Renal Disease (MDRD) formula at screening or baseline visit. Acute coronary syndrome, ischemic stroke or TIA, coronary revascularization or peripheral arterial revascularization procedure or amputation due to atherosclerotic disease < 3 months prior to the screening or baseline visit. Planned or expected cardiac, cerebrovascular or peripheral artery surgery or coronary revascularization within the study duration. Heart failure New York Heart Association (NYHA) class IV at screening or baseline visit. History of malignancy that required surgery (excluding local and wide-local excision), radiation therapy and/or systemic therapy during the 3 years prior to screening or baseline visit. Participant with myopathy at screening or baseline visit. Participant receiving concomitant ciclosporin at screening or baseline visit. Participants that are predisposed to the development of renal failure secondary to rhabdomyolysis (e.g. sepsis, hypotension, major surgery, trauma, severe metabolic, endocrine and electrolyte disorders; or uncontrolled seizures). Participants with rare hereditary problems of galactose intolerance, the Lapp lactase deficiency or glucose-galactose-malabsorption. Unwillingness or inability (e.g. physical or cognitive) to comply with study procedures (including study visits, fasting blood draws and compliance with study treatment regimens), and medication administration (injections) and schedule. Participant should be able and willing to read, understand and answer questionnaires. Any surgical or medical condition, which in the opinion of the investigator, may place the participant at higher risk from his/her participation in the study, or is likely to prevent the participant from complying with the requirements of the study or completing the study at screening or baseline visit. Use of other investigational drugs within 5 half-lives, 30 days or until the expected pharmacodynamic effect has returned to baseline (e.g. biologics), whichever is longer or longer if required by local regulation, prior to screening visit. Pregnant or nursing (lactating) women at screening or baseline visit.  Women of child-bearing potential, defined as all women physiologically capable of becoming pregnant, unless they are using highly effective methods of contraception while taking study treatment, which includes rosuvastatin, and for 5 days (= 5 times the terminal half-life of rosuvastatin) after stopping medication. Highly effective contraception methods include:  Total abstinence (when this is in line with the preferred and usual lifestyle of the participant. Periodic abstinence (e.g. calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception. Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy), total hysterectomy, or bilateral tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment. Male sterilization (at least 6 months prior to screening). For female participants on the study, the vasectomized male partner should be the sole partner for that participant. Use of oral, (estrogen and progesterone), injected, or implanted hormonal methods of contraception or placement of an intrauterine device (IUD) or intrauterine system (IUS), or other forms of hormonal contraception that have comparable efficacy (failure rate < 1%), for example hormone vaginal ring or transdermal hormone contraception.  In case of use of oral contraception women should have been stable on the same pill for a minimum of 3 months before taking study treatment.  Women are considered post-menopausal if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate history of vasomotor symptoms). Women are considered not of child bearing potential if they are post-menopausal or have had surgical bilateral oophorectomy (with or without hysterectomy), total hysterectomy or bilateral tubal ligation at least six weeks ago. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow-up hormone level assessments and she is considered not of child bearing potential.  If local regulations deviate from the contraception methods listed above to prevent pregnancy, local regulations apply and will be described in the local ICF.