Efficacy and Safety of Encaleret Compared to Standard of Care in Participants with ADH1

The primary purpose of the study is to understand the effectiveness, safety, and tolerability of encaleret when compared to standard of care (SoC) treatment in participants with Autosomal Dominant Hypocalcemia Type 1 (ADH1).

ADH1 is a rare genetic form of hypoparathyroidism. ADH1 may be passed down from affected parents to their children.

The main portion of the study is divided into a Screening Period and 3 Periods followed by an optional Long-Term Extension (LTE). The estimated duration of this main portion of the study is approximately 12 months. The duration of the LTE is approximately 48 months.

Participants will enter an up-to-6-week Screening period and once confirmation of all Inclusion/Exclusion criteria transition into an up-to-15-week standard of care (SoC) optimization phase. The eligible participants will enter Period 1 after completing the SoC optimization phase.

Period 1 is the 4-week SoC Maintenance period of the study during which the SoC dose will only be adjusted to address potential safety concerns such as hypocalcemia or hypercalcemia.

After completion of Period 1, eligible participants will enter Period 2 and will be randomized to receive either encaleret or SoC treatment for 20 weeks. Both the investigator and participant will know whether the participant was randomized to the encaleret treatment arm or SoC treatment arm. During Period 2, encaleret or SoC will be adjusted based on blood calcium levels.

After completion of Period 2, participants will proceed to Period 3, the 4-week dose maintenance period.

Following completion of Period 3, participants from CLTX-305-302 may enter the LTE. Those who completed CLTX-305-201 (NCT04581629) are also eligible to continue in the LTE. Participants will receive encaleret treatment for approximately 48 months, or 72 months for participants who transitioned from CLTX-305-201, or until a participant has access to commercial encaleret, or the Sponsor decides to end the study, whichever occurs first.

Eligibility Criteria:
Key Inclusion Criteria:

1. Participants must have a documented pathogenic or likely pathogenic activating variant, or variant of uncertain significance, of the calcium sensing receptor (CASR) gene associated with biochemical findings of hypoparathyroidism.
2. Participants must have a documented history of symptoms or signs of ADH1.
3. Participants 16 to \<18 years old must have closed growth plates on hand radiograph.
4. Participants treated with thiazide diuretics must discontinue thiazides for at least 14 days prior to SoC Optimization Visit 1 through Week 24 (Period 3). When the thiazide is being used as an antihypertensive, alternative therapy will be prescribed by the Investigator as needed.
5. Participants treated with phosphate binders (other than calcium salts) must discontinue the phosphate binders at least one day prior to the SoC Optimization Visit 1.
6. Participants treated with magnesium or potassium supplements must be willing to discontinue such treatment prior to the first dose of encaleret.
7. Participants treated with potassium-sparing diuretics must be willing to discontinue such treatment prior to the first dose of encaleret.
8. Participants must meet SoC Optimization criteria as defined in the protocol.

Key Exclusion Criteria:

1. History of hypocalcemic seizure within the past 3 months preceding Screening.
2. History of thyroid or parathyroid surgery.
3. History of renal transplantation.
4. Pregnant or nursing (lactating) women, where pregnancy is confirmed by a positive beta-human chorionic gonadotropin (β-hCG) laboratory test.
5. History of treatment with parathyroid hormone (PTH) 1-84 or 1-34 within the 2 months preceding Screening and requiring SoC doses exceeding \>1.2× their pre-PTH treatment total daily doses or bone turnover markers, Collagen cross-linked C-telopeptide (CTx )and Procollagen type 1 N-propeptide (P1NP), \> upper limit of normal for sex, age (men only) and menopausal status (women only).
6. Blood 25-OH Vitamin D level \<25 nanograms (ng)/milliliter (mL).
7. Estimated glomerular filtration rate (eGFR) \<30 mL/minute/1.73 m\^2 using chronic kidney disease-EPI creatinine equation refit without the race variable (chronic kidney disease-EPI creatinine equation refit without the race variable \[CKD-EPIcr_R\]) (for participants \<18 years old the Bedside Schwartz equation should be used).
8. Participants with positive Hepatitis B surface antigen (HBsAg), Hepatitis A immunoglobulin M (IgM), or human immunodeficiency virus (HIV) viral serology test at the Screening Visit. Participants who are in complete remission from Hepatitis C virus (HCV) as evidenced by sensitive assay ≥12 weeks after completion of HCV therapy may participate in the study.

Note: Other protocol defined Inclusion/Exclusion criteria may apply.