The HArps-n red Dwarf Exoplanet Survey is providing a major contribution to the widening of the current statistics of low-mass planets, through the in-depth analysis of precise radial velocity measurements in a narrow range of spectral sub-types. Using the HARPS-N spectrograph we reach the precision needed to detect small planets with a few earth masses. Our survey is mainly focused on the M-dwarf population of the northern hemisphere. As part of that programme, we obtained radial velocity measurements of Gl686, an M1 dwarf at d=8.2pc. These measurements show a dispersion much in excess of their internal errors. The analysis of data obtained within an intensive observing campaign, demonstrates that the excess dispersion is due to a coherent signal, with a period of 15.53d. Almost simultaneous photometric observations were carried out within the APACHE and EXORAP programmes to characterize the stellar activity and to distinguish periodic variations related to activity from signals due to the presence of planetary companions, complemented also with ASAS photometric data. We used a Bayesian framework to estimate the orbital parameters and the planet minimum mass, and to properly treat the activity noise. We took advantage of the available radial velocity measurements for this target from other observing campaigns. The analysis of the radial velocity composite time series from the HIRES, HARPS and HARPS-N spectrographs, consisting of 198 measurements taken over 20 years, enabled us to address the nature of periodic signals and also to characterize stellar physical parameters (mass, temperature and rotation). We report the discovery of a super-Earth orbiting at a distance of 0.092AU from the host star Gl686. Gl686 b has a minimum mass of 7.1+/-0.9M_{Earth} and an orbital period of 15.532+/-0.002d. The analysis of the activity indexes, correlated noise through a Gaussian process framework and photometry, provides an estimate of the stellar rotation period at 37d, and highlights the variability of the spot configuration during the long timespan covering 20yrs. The observed periodicities around 2000d likely point to the existence of an activity cycle.