Key Inclusion Criteria:  Clinical diagnosis of familial partial lipodystrophy as defined in the protocol Fasting leptin level ≤20.0 ng/ml, as determined during the screening period Presence of significant metabolic abnormalities related to glucose and triglycerides (TGs) as defined in the protocol Stable body weight within the 3 months prior to screening (no gain or loss of >5% current weight) Stable diet during the past 3 months defined as no major change in macronutrient composition (eg, starting or stopping diets such as Atkins, Paleo, Vegetarianism, Veganism) No clinically meaningful change in medication regimen in the 3 months prior to screening as defined in the protocol  Key Exclusion Criteria:  Treatment with metreleptin within 3 months of the screening visit Patients with a diagnosis of generalized lipodystrophy Patients with a diagnosis of acquired lipodystrophy Pregnant or breastfeeding women  NOTE: Other protocol defined inclusion/exclusion criteria apply