The site lies between the present steading and the sea, the main structure being the excavated chapel. The published souterrain can be seen below its floor level emerging from the back at your right and coming 'out' from under the wall at a slight angle. It has been filled in with stones, as have two passages in the cliff face far to the E of the main site (I do not know their date) - presumably all by the excavators. It could be me, but I did not see the 'tunnel' exiting the cliff.
RCAHMS NMRS record no. HY50SE 3 at HY57460413 mostly survives as a 10th century chapel and burial-ground, the former turned into a 16th C laird's house, but two souterrains were found beneath the chapel.
Only one has been published. Though it is described as a 10m long curved chamber running E/W, leaving at the cliff edge, it actually runs more N/S at the coast and runs to about 50' i.e. continuing underground for some distance past the chapel. This latter information comes from a website started by two ex-diggers (http://www.hopkinsweb.org.uk/orkney/), with the earth-house shown as a tunnel in the plans incorporated within their diaries. Unfortunately this only covers the dig's first two years. Apart from this there is very little published about the Newark excavations, either on paper or online, excepting the NMRS details. Which is a shame as the last entry is the discovery of a skeleton lying on a slab that may have served a platform.