In this comprehensive study, we present results of bulk measurements (magnetization, specific heat, ac susceptibility, thermal expansion, and magnetostriction) combined with local methods such as nuclear magnetic resonance (Na23 NMR) and electron spin resonance (ESR) and simulations (McPhase) on polycrystalline and single-crystalline NaGdS2 samples. The rare-earth delafossite NaGdS2 is a triangular-lattice magnet with S=7/2 spin-only Gd3+ moments with suppressed single-ion anisotropy. In our study, we estimate that NaGdS2 has a weak antiferromagnetic exchange (JH/kB≈52mK) and signs of long-range magnetic order are absent down to lowest temperature. However, indications of short range magnetic order are found below 180 mK in the ac susceptibility and thermal expansion. Our results indicate an interplay of Heisenberg-type and dipolar exchange. Due to the large moment of the Gd3+ ions, one expects a strong impact of the dipolar coupling in NaGdS2, in contrast to the related NaYbS2. ESR and Na23 NMR measurements, indeed, indicate the formation of short-range ferromagnetic correlations. NaGdS2 appears to be a rare system, in which magnetic order is suppressed by a competition between Heisenberg and dipolar interactions.