Context. Stars that have evolved off the main sequence are crucial for expanding the frontiers of knowledge on exoplanets toward higher stellar masses and for constraining star-planet interaction mechanisms. These stars have an intrinsic activity, however, which complicates the interpretation of precise radial velocity (RV) measurements, and therefore they are often avoided in planet searches. Over the past ten years, we have monitored about 1000 evolved stars for RV variations in search for low-mass companions under the Penn State - Toruń Centre for Astronomy Planet Search program with the Hobby-Eberly Telescope. Selected prospective candidates that required higher RV precision measurements have been followed with HARPS-N at the 3.6 m Telescopio Nazionale Galileo. Aims: We aim to detect planetary systems around evolved stars, to be able to build sound statistics on the frequency and intrinsic nature of these systems, and to deliver in-depth studies of selected planetary systems with evidence of star-planet interaction processes. Methods: We obtained 69 epochs of precise RV measurements for TYC 1422-614-1 collected over 3651 days with the Hobby-Eberly Telescope, and 17 epochs of ultra-precise HARPS-N data collected over 408 days. We complemented these RV data with photometric time-series from the All Sky Automatic Survey archive. Results: We report the discovery of a multiple planetary system around the evolved K2 giant star TYC 1422-614-1. The system orbiting the 1.15 M⊙ star is composed of a planet with mass msini = 2.5 MJ in a 0.69 AU orbit, and a planet or brown dwarf with msini = 10 MJ in an orbit of 1.37 AU. The multiple planetary system orbiting TYC 1422-614-1 is the first finding of the TAPAS project, a HARPS-N monitoring of evolved planetary systems identified with the Hobby-Eberly Telescope. Based on observations obtained with the Hobby-Eberly Telescope, which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen.Based on observations made with the Italian Telescopio Nazionale Galileo (TNG) operated on the island of La Palma by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.Tables 2 and 3 are available in electronic form at http://www.aanda.org