Detection and characterisation of Jovian analogues in precision radial velocity (RV) measurements is gaining momentum due to the constantly increasing observational baseline of Doppler surveys. The occurrence rate of Jovian-mass exoplanets is crucial for understanding the architecture of planetary systems. However, long-period RV signals in Doppler surveys could also be induced by stellar magnetic cycles, leading to misinterpretations of planetary candidates. We investigate the long-term RV variability in the K-dwarf star GJ1137 (HD93083, HIP52521), a known Saturn-mass exoplanet host, and assess the role of stellar activity in shaping the observed signals. We analyse 13 years of archival high-precision spectroscopic observations obtained with the High Accuracy Radial velocity Planet Searcher spectrograph (HARPS). We performed an extensive spectroscopic analysis of the stellar activity indicators and applied an RV modelling approach, incorporating Keplerian fits, Gaussian process regression as a proxy for stellar activity, and other stellar activity diagnostics. Furthermore, we refined the orbital parameters and the minimum mass of the known exoplanet GJ 1137 b and searched for additional planetary candidates in the system. We detect a long-period RV signal that, if interpreted as planetary, would suggest the presence of a Jovian-analogue companion. However, our spectroscopic activity analysis provides strong evidence that this variability is induced by the star's long-term magnetic cycle P_cyc_=5870^+480^-350 days rather than by an orbiting planet. The signal is detected in both the full width at half maximum (FWHM) of the cross-correlation function and the chromospheric activity index logR'HK. We measure the stellar rotation period to P_rot=32.3^+1.2^-1.3 days and identify a significant short-period RV signal, which we attribute to a Super Earth with a period of 9.6412^+12^-11 days and a minimum mass of 5.12^+0.70^-0.69 Earth masses, making GJ 1137 a multiple-planet system.