Participants must have histologically or cytologically confirmed prostate cancer, or unequivocal clinical evidence of mHSPC (eg. elevated PSA with lesions consistent with metastatic prostate cancer).

Age ≥18 years.

Participants must have mHSPC (either de novo or relapse after prior local therapy), as defined by extrapelvic nodal and/or visceral and/or bone lesions consistent with metastatic disease and seen on CT, bone scan and/or MRI. If participants have relapsed after prior local therapy, they must not have had systemic therapy in the past 6 months prior to study registration.

Serum testosterone \>150 ng/dL.

Planned initiation of systemic therapy with ADT (androgen deprivation therapy) and an AR pathway inhibitor (abiraterone, enzalutamide, apalutamide, darolutamide) ± docetaxel. Initiation of systemic therapy up to 14 days prior to the baseline 18F-rhPSMA-7.3 PSMA-PET/CT is permitted.

Ability and willingness to comply with the study procedures.

Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational agent are eligible for this trial.

The effects of 18F-rhPSMA-7.3 on the developing human fetus are unknown. For this reason and because radiopharmaceutical agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for 24 hours after each 18F-rhPSMA-7.3 PSMA-PET scan.

Ability to understand and the willingness to sign a written informed consent document.

Systemic therapies other than ADT (GnRH/LHRH agonists or antagonists), AR pathways inhibitors (abiraterone, enzalutamide, apalutamide, darolutamide) and docetaxel are not permitted to be administered during the study period.

Radiation to the prostate and/or metastatic sites prior to the 6-month PET scan is not permitted.

Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.

Contraindications to PET/CT, including severe claustrophobia.

History of allergic reactions attributed to compounds of similar chemical or biologic composition to 18F-rhPSMA-7.3.

Any past or current condition that, in the opinion of the study investigators, would confound the results of the study or would pose additional risk or burden to the patient by their participation in the study.