Study of SHP639 Eye Drops in Adults With High Eye Pressure or Primary Open-angle Glaucoma

Inclusion Criteria: 1. Participants must provide written, signed and dated informed consent to participate in the study in accordance with the International Council for Harmonisation (ICH) Good Clinical Practice (GCP) Guideline E6(R1) and applicable regulations, before completing any study-related procedures. 2. Participants must be aged from 18 through 90 at the time of consent. This inclusion criterion will only be assessed at the screening visit. 3. Participants must have ocular hypertension (OHT) or stable early primary open-angle glaucoma (POAG) in both eyes with acceptable Humphrey visual fields (HVF). Early POAG for this protocol is defined as healthy appearing anterior chamber angles (Shaffer classification system grade 3 or 4) and focal and/or generalized thinning of the optic disc rim characteristic of glaucomatous disease. An acceptable HVF must have been performed within approximately one year of screening, have a false-positive rate of 25 percent (%) maximum, false-negative rate of 25% maximum, and fixation loss rate of 33% maximum, and mean deviation of no worse than -6.00 decibels (dB). 4. On Day -1, participants must have a mean IOP of greater than or equal to (\>=) 24 millimeter of mercury (mmHg) at 8:00 AM and a mean IOP of \>= 22 mmHg at 10:00 AM in at least 1 eye, with an IOP difference of less than (\<) 4 mmHg between eyes at both of these time points. If only 1 eye meets this criterion, then it will be the designated study eye for pharmacodynamic analysis; this eye will also be used for dosing in Cohort A single-dose treatment period (SDTP). 5. Participants must have a best-corrected visual acuity (BCVA) in both eyes of 65 letters on the Early Treatment Diabetic Retinopathy Study chart (Snellen equivalent approximately \[∼\] 20/60) or better at the screening and baseline assessments. 6. Participants must be males or females who are non-pregnant and non-lactating at screening (negative serum beta-human chorionic gonadotropin \[beta-hCG\]); if sexually active during the study, they must agree to comply with the applicable contraceptive requirements throughout the study period and for 60 days following the last dose of investigational product. 7. Participants must have a satisfactory medical assessment with no clinically significant or relevant abnormalities as determined by medical history, physical examination, and clinical and laboratory evaluation (hematology, biochemistry, urinalysis) as assessed by the investigator. 8. Participants must understand and be able, willing, and likely to fully comply with study procedures and restrictions. 9. Participants must be non-smokers or have had stable use of tobacco or nicotine-containing products for a 3-month period before signing the informed consent form (ICF). 10. Participants who drink alcohol must have had stable use of alcohol for a 3-month period before signing the ICF. Exclusion Criteria: 1. Participant has an anatomically narrow angle, synechiae or evidence of prior inflammation, angle closure glaucoma, normal tension glaucoma, pseudoexfoliation syndrome or pigmentary dispersion syndrome with or without glaucoma, or secondary glaucoma. 2. Participant has corneal endothelial cell counts of less than 2000 cells per millimeter\^2 (measured by noncontact specular microscopy) at the screening or baseline assessments. 3. Participant has central corneal thickness less than 500 micrometer (mcm) or greater than 620 mcm at the screening or baseline assessments. 4. Participant has IOP greater than 32 mmHg in either eye before randomization. 5. Participant has used topical ocular hypotensive medications as follows: prostaglandin analogs, beta-adrenoceptor antagonists, alpha-adrenergic agonists, or epinephrine-related medications within 4 weeks before the first dose of investigational product; or pilocarpine or carbonic anhydrase inhibitors within 7 days before the first dose of investigational product. 6. Participant has a history of angle closure, ocular surgery, microinvasive glaucoma surgery device insertion, or laser surgery, except for the following procedures, which are allowed: uncomplicated cataract surgery, laser peripheral iridotomy with resultant angle of Shaffer grade 3 or 4, and postcataract neodymium-doped yttrium-aluminum-garnet (Nd:YAG) laser posterior capsulotomy. Cataract surgery and other procedures must have occurred a minimum of 3 months before randomization. 7. Participant has a history of significant ocular trauma or ocular disease including but not limited to moderate to severe dry eye disease that requires chronic treatment or punctal plugs. 8. Participant has evidence of ocular infection, inflammation, degeneration, or dystrophy at the screening or baseline assessments, including but not limited to moderate to severe blepharitis (mild blepharitis is allowed), conjunctivitis (allergic or infectious), corneal dystrophy (epithelial, stromal, or endothelial), corneal haze of grade 1 or greater based on the Hwang Grading Scale of Corneal Haze, corneal opacities, keratitis, uveitis, or vitritis. 9. Participant has retinal disease including but not limited to: moderate or severe non-proliferative diabetic retinopathy (NPDR) (early NPDR is allowed), proliferative diabetic retinopathy, intermediate or advanced dry age-related macular degeneration (AMD) (early dry AMD is allowed), all geographic atrophy, or all wet AMD. 10. Participant has any non-glaucomatous optic neuropathy or other significant non-glaucomatous ocular disease that is likely to affect visual function. 11. Participant has any corneal or ocular surface pathology in either eye that prevents proper IOP measurement, pachymetry, or other study data collection procedures. 12. Participant has had changes to their existing prescription medication regimen for chronic disease, including those medicines that affect IOP, within 14 days or 5 half-lives before screening, whichever is longer. 13. Participant has started any new prescription drug medication for chronic disease, including those medicines that affect IOP, within 14 days or 5 half-lives before screening, whichever is longer. 14. Participant has a history of corticosteroid use within 3 months before randomization, except for non-periocular dermatologic use, which is allowed. 15. Participant has used belladonna alkaloids (scopolamine, hyoscamine, atropine) within 7 days prior to randomization, cannabinoids or opioids within 28 days before randomization, or B-type natriuretic peptides within the past year before randomization; or a participant has an anticipated need for any of the aforementioned drugs/drug categories during the study. 16. Participant has used amantadine within 28 days before randomization. 17. Participant is unable to discontinue contact lens use during and for 60 minutes following instillation of study medication, during ophthalmologic examinations, and during study visits. 18. Participant has a current or relevant history of any physical, medical, mental, or psychiatric illness, disorder, or condition that may require treatment during the study and/or that may interfere with the participant complying with the study rules and procedures or completing the study. 19. Participant has any condition that presents undue risk from use of the investigational product, assessment tools, or procedures. 20. Participant is a woman who is pregnant (positive serum beta-hCG pregnancy test at the time of screening), lactating, or less than 90 days post-partum at randomization. 21. Participant has donated blood within 60 days before first dose of investigational product. 22. Participant has donated plasma within 28 days before first dose of investigational product. 23. Participant has used another investigational product within 30 days before the first dose of investigational product or is actively enrolled in a drug or vaccine clinical study. 24. Participant has a positive human immunodeficiency virus (HIV), hepatitis B surface antigen (HBsAg), or hepatitis C virus (HCV) antibodies screen. 25. Participant has a positive drugs of abuse screen or alcohol breathalyzer test. 26. Participant has been previously enrolled in this study. 27. Participant has known hypersensitivity or allergy to any of the ingredients of the investigational product. 28. Participant consumes more than 21 units of alcohol per week or is unable to refrain from alcohol consumption within 48 hours before a scheduled visit. (1 alcohol unit=1 beer or 1 wine \[5 ounce per 150 milliliter\] or 1 liquor \[1.5 ounce per 40 milliliter\] or 0.75 ounce alcohol.) 29. Participant is unable to refrain from tobacco or any products containing nicotine within 8 hours before a scheduled visit.