Detecting a planetary companion in a short-period orbit through radio emission from the interaction with its host star is a new prospect in exoplanet science. A tantalising signal was found by Vedantham et al. (2020NatAs...4..577V) close to the low-mass stellar system GJ 1151 using LOFAR observations. We studied spectroscopic time-series data of GJ 1151 to search for planetary companions and to investigate possible signatures of stellar magnetic activity and to find possible explanations for the radio signal. We used the combined radial velocities measured from spectra acquired with the CARMENES, HARPS-N, and HPF instruments, extracted activity indices from those spectra in order to mitigate the impact of stellar magnetic activity on the data, and analysed in detail Gaia astrometry, and all available photometric time series coming from the MEarth and ASAS-SN surveys. We found a M>10.6M_Earth_ companion to GJ 1151 in a 390-d orbit at a separation of 0.57au. Evidence for a second modulation is also present and could be due to long-term magnetic variability, or a second (substellar) companion. The star shows episodes of elevated magnetic activity, one of which could be linked to the observed LOFAR radio emission. We show that it is highly unlikely that the detected GJ 1151 b, or any additional outer companion can be the source of the detected signal. We cannot firmly rule out the explanation given by Vedantham et al. (2020NatAs...4..577V), as we establish an upper limit of 1.2M_Earth_ for the minimum mass of an undetected short-period planet that could be related to the radio emission.