The synergy between different detection methods is a key asset in exoplanetology that allows the precise characterization of detected exoplanets and robust constraints even in the case of a non-detection. The interplay between imaging, radial velocities and astrometry has recently 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 a significant proper motion anomaly. We focus on HD\,57625, a F8 star for which we determine a $ Ga age, exhibiting significant astrometric acceleration and for which archival radial velocities indicate a previously undetected massive long-period companion. We analysed 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 characterised the companion causing 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 planetary companion with an orbital separation of and an eccentricity of HD\,57625\,b joins the small but growing population of giant planets on outer orbits with a true mass determination provided by the synergic usage of multiple detection methods. This again proves the importance of a multi-technique analysis in providing a robust characterization of planetary companions.
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