The objective of the ESK-001-018 long term extension is to evaluate the safety and efficacy of ESK-001 over time. The scientific questions it aims to answer are: * How safe is taking ESK-001 long-term in people with moderate to severe plaque psoriasis? * Does taking ESK-001 long-term reduce the severity of people's plaque psoriasis? Patients will enter the long-term extension study following completion of one of the parent studies (ESK-001-016 or ESK-001-017) and will receive open-label ESK-001 twice daily for 24 weeks. After 24 weeks, the first 200 patients meeting at least PASI-75 clinical response will be randomly assigned to receive ESK-001 or placebo. At any point during this time, the patients losing the initial clinical response may return to the open-label ESK-001 treatment. Patients who complete Week 48 will return to open-label ESK-001 treatment and they will receive ESK-001 until the end of the study or discontinuation. All the remaining patients not meeting the entry criteria for the randomized withdrawal phase will continue to receive open-label ESK-001 for the remainder of the study. Patients taking part in the study must be men or women aged at least 18 years old and have completed a previous (parent) study of ESK-001 in moderate to severe plaque psoriasis. Patients must consent and agree to: * ensure drug daily compliance until end of study or discontinuation. * visit the clinic for checkups and assessments. * provide blood and urine samples.