Seismic monitoring of the cryosphere is mostly done with land seismometers on the surface of ice masses. Seismic monitoring beneath sea ice at the bottom of ice-covered oceans has hardly been attempted, because ocean bottom seismometers (OBS) are difficult to recover in perennial sea ice. As a result, for example the tectonic activity of the Arctic mid-ocean ridge system is poorly known. Recently, ambient seismic noise in long-term seismic records proved a useful tool to monitor the state of the sea ice cover. From September 2018 - September 2019, we deployed a trial network of 4 broadband OBS in Arctic sea ice. OBS were positioned at distances of 10 km at a water depth of 4 km on eastern Gakkel Ridge. Station noise levels from power spectral density analysis are considerably lower for sub-ice stations than for OBS in the Greenland Sea and are comparable to those of Arctic land stations. The network was designed to record local earthquakes along Gakkel Ridge, but it also yielded valuable data on the sub-ice ambient seismic noise in the Arctic Ocean. Spectrograms covering the entire deployment reveal pronounced seasonality in different frequency bands: Above 5 Hz, noise levels increase when sea ice cover is present. In addition, anthropogenic noise is prominently seen. The secondary microseismic noise peak has two clearly separable components with opposite seasonal evolution. Microseisms at 3-10 s periods relate to swell events outside the Arctic Ocean with a higher incidence of such events during winter time. In contrast, secondary microseisms originating in the Arctic Ocean peak in September during the annual sea ice minimum. Their periods increase from 0.5 s to 5 s as the fetch area for wave evolution increases from June to September.