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The synergy between different detection methods is a key asset in exoplanetology, allowing for both precise characterization of detected exoplanets and robust constraints even in the case of non-detection. Recently, the interplay between imaging, radial velocities and astrometry has produced significant advancements in exoplanetary science. We report a first result of an ongoing survey performed with SHARK-NIR, the new high-contrast near-infrared imaging camera at the Large Binocular Telescope, in parallel with LBTI/LMIRCam in order to detect planetary companions around stars with significant proper motion anomaly. In this work we focus on HD 57625, a F8 star for which we determine a $4.8^{+3.7}_{-2.9}$Ga age, exhibiting significant astrometric acceleration and for which archival radial velocities hint at the presence of a previously undetected massive long-period companion. We analyse the imaging data we collected with SHARK-NIR and LMIRCam in synergy with the available public SOPHIE radial velocity time series and Hipparcos-Gaia proper motion anomaly. With this joint multi-technique analysis, we aim at characterizing the companion responsible for the astrometric and radial velocity signals. The imaging observations result in a non-detection, indicating the companion to be in the substellar regime. This is confirmed by the synergic analysis of archival radial velocity and astrometric measurements resulting in the detection of HD 57625 b, a ${8.43}_{-0.91}^{+1.10}$M$_{\rm Jup}$ planetary companion with an orbital separation of ${5.70}_{-0.13}^{+0.14}$au and ${0.52}_{-0.03}^{+0.04}$ eccentricity. HD 57625 b joins the small but growing population of giant planets in outer orbits with true mass determination provided by the synergic usage of multiple detection methods, proving once again the importance of multi-technique analysis in providing robust characterization of planetary companions., Comment: 12 pages, 8 figures, accepted for publication in A&A