A Study Evaluating the Effects of GLPG3970 Given as an Oral Treatment for 12 Weeks in Adults With Active Primary Sjögren's Syndrome (pSS)

Key Inclusion Criteria: 1. Documented diagnosis of pSS for \<10 years prior to screening AND defined by the classification criteria \>=4 described by the American College of Rheumatology - European League Against Rheumatism (ACR-EULAR). 2. Participant has an ESSDAI score \>=5 assessed on 7 domains: constitutional, lymphadenopathy, glandular, articular, cutaneous, hematological, and biological. 3. Participant has an ESSPRI score \>=5. 4. Participant has stimulated whole salivary flow rate of \>=0.1 milliliter per minute (mL/min). 5. Participant has positive serum titers of anti-Sjögren's-syndrome-related antigen A (anti-SS-A)/Ro and/or anti-SS-B/La antibodies. 6. Participants already on treatment should be on stable standard of care (SoC) for at least 4 weeks prior to first investigational product (IP) dosing. The following SoC medications are permitted: * Corticosteroids \<=7.5 mg/day (prednisone or equivalent); AND/OR * Non-steroidal anti-inflammatory drugs (NSAIDs); AND/OR * One single antimalarial at a stable dose (hydroxychloroquine \<=400 mg/day; quinacrine 100 mg/kg/day, or chloroquine \<=250 mg/day); AND/OR * One single immunosuppressant at a stable dose (methotrexate \[MTX\] \<=10 mg/week or azathioprine \[AZA\] \<=2 mg/kg/day); AND/OR * One single cholinergic stimulant at a stable dose (e.g., pilocarpine, cevimeline). 7. Female participant of childbearing potential must have a negative highly sensitive (serum beta human chorionic gonadotropin or urine dipstick) pregnancy test. 8. Female participant of childbearing potential or male participant must agree to use highly effective contraception/preventive exposure measures. Key Exclusion Criteria: 1. Secondary Sjögren's syndrome according to the ACR-EULAR (2016) classification. 2. History or presence of unstable condition not related to Sjögren's Syndrome that, in the opinion of the investigator, could constitute an unacceptable risk when taking the IP or interfere with the interpretation of data. 3. Participant has any active systemic infection within 2 weeks prior to first IP dosing, or poorly controlled chronic cardiac, pulmonary, or renal disease. 4. Participant has a known or suspected history of or a current immunosuppressive condition, or a history of opportunistic infections (e.g., human immunodeficiency virus \[HIV\] infection, histoplasmosis, listeriosis, coccidioidomycosis, pneumocystosis, aspergillosis). 5. Participant has a chronic hepatitis B virus (HBV) infection, as defined by persistent HBV surface antigen (HBsAg) positivity. Participant has hepatitis C virus (HCV) infection, as defined by positive HCV antibody at screening and detectable HCV viremia. Participants with positive HCV antibody must undergo reflex HCV ribonucleic acid (RNA) testing, and participants with HCV RNA positivity will be excluded. Participants with positive HCV antibody and negative HCV RNA are eligible. 6. Participant testing positive for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection as detected at screening based on real time polymerase chain reaction (RT-PCR) or at baseline based on immunoglobulin M (IgM) immunoassay, or participants who have been in contact with SARS-CoV-2 infected individuals in the 2 weeks prior to first dosing of IP. Participants presenting any signs or symptoms of SARS-CoV-2 infection, as detected prior to first IP dosing following careful physical examination (e.g., cough, fever, headaches, fatigue, dyspnea, myalgia, anosmia, dysgeusia, anorexia, sore throat, etc). In addition, any other locally applicable standard diagnostic criteria may also apply to rule out SARS-CoV-2 infection. 7. Participant has taken any disallowed therapies: * Mycophenolate mofetil (MMF) within a week prior to screening. * Cyclosporine/Tacrolimus within a week prior to screening. * Cyclophosphamide within 6 months prior to screening. * Ocular medicines (e.g., topical cyclosporine, topical NSAIDs/ corticosteroids) for at least 4 weeks prior to screening, except for a sporadic use. * Biologics such as, but not limited to, rituximab, abatacept, and any other unapproved biologic within 6 months prior to screening. * Plasmapheresis within 12 weeks prior to screening. * Plasma exchange within 12 weeks prior to screening. * Intravenous immunoglobulin (IVIG) therapy within 24 weeks prior to screening. * Other prohibited medications within 2 weeks or 5 half-lives, whichever is longer, prior to first IP dosing. 8. Concurrent use of anticholinergic agents or any other medication known to cause dry mouth/dry eyes that, in the opinion of the investigator, are a contributing factor to the participant's dryness and/or use of anticholinergic agents not contributing to this dryness, if not stable at least 4 weeks prior to screening. 9. Participant has a history of tuberculosis (TB) diagnosis or evidence of active or latent infection with Mycobacterium tuberculosis. 10. Participant has a history of lymphoma or any malignancy within the past 5 years prior to screening with the exception of excised and curatively treated non-metastatic basal cell carcinoma or squamous cell carcinoma of the skin or carcinoma in situ of cervix which is considered cured with minimal risk of recurrence. 11. Participant has severe organ manifestation or life-threatening condition, or has planned a surgery during the study. Note: Other protocol-defined Inclusion/Exclusion criteria may apply.