We analysed temporal variations of trace element concentrations in groundwater from a 101 m-deep borehole (HA01) in northern Iceland during 2010–2018 and compared them with seismic and volcanic events that occurred in the same period to identify potential hydrogeochemical precursors. An increase of B, Al, V, Li and Mo concentrations started from eight months to one month before the 2014 Bárðarbunga eruption (~115 km from HA01), a major rifting event in central Iceland, while Ga and V concentrations began to increase one day and one month after the onset of the event, respectively. We also found that concentrations of some trace elements (Li, B, Ga, Mo, Sr, Rb and Fe) significantly increased before an M_w 5.0 earthquake that occurred ~80 km from the borehole in 2018. However, other notable hydrogeochemical changes were detected during the monitoring period without apparent correlation with the seismic and volcanic events in the region. This study shows that the systematic long-term hydrogeochemical monitoring in seismic and volcanic areas is critical to advance the science of seismic and eruptive precursors. Furthermore, the use of statistical tools, such as Principal Component Analysis (PCA) and Change Point (CP) detection can help identify the most useful chemical elements and validate the trend variability of those elements in the time series, reducing arbitrary choices of pre-seismic and pre-volcanic hydrogeochemical anomalies as potential precursors.