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We report on the result of a campaign to monitor 25 HATSouth candidates usingthe K2 space telescope during Campaign 7 of the K2 mission. We discoverHATS-36b (EPIC 215969174b), a hot Jupiter with a mass of 2.79$\pm$0.40 M$_J$and a radius of 1.263$\pm$0.045 R$_J$ which transits a solar-type G0V star(V=14.386) in a 4.1752d period. We also refine the properties of threepreviously discovered HATSouth transiting planets (HATS-9b, HATS-11b, andHATS-12b) and search the K2 data for TTVs and additional transiting planets inthese systems. In addition we also report on a further three systems thatremain as Jupiter-radius transiting exoplanet candidates. These candidates donot have determined masses, however pass all of our other vetting observations.Finally we report on the 18 candidates which we are now able to classify aseclipsing binary or blended eclipsing binary systems based on a combination ofthe HATSouth data, the K2 data, and follow-up ground-based photometry andspectroscopy. These range in periods from 0.7 days to 16.7 days, and down to1.5 mmag in eclipse depths. Our results show the power of combiningground-based imaging and spectroscopy with higher precision space-basedphotometry, and serve as an illustration as to what will be possible whencombining ground-based observations with TESS data.

HATS-36b and 24 other transiting/eclipsing systems from the HATSouth - K2 Campaign 7 program