  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. Recently, a tantalising signal was found close to the low-mass stellar
system GJ 1151 using LOFAR observations. We studied spectroscopic time-series
data of GJ 1151 in order to search for planetary companions, 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 performed a detailed analysis of
Gaia astrometry and all available photometric time series coming from the
MEarth and ASAS-SN surveys. We found a M$>$10.6 M$_{\oplus}$ companion to GJ
1151 in a 390d orbit at a separation of 0.57 au. Evidence for a second
modulation is also present; this 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 is the source of the detected signal. We cannot
firmly rule out the suggested explanation of an undetected short-period planet
that could be related to the radio emission, as we establish an upper limit of
1.2 M$_{\oplus}$ for the minimum mass.
