HIP 65426 b is a recently discovered exoplanet imaged during the course of the SPHERE-SHINE survey. Here we present new L′ and M′ observations of the planet from the NACO instrument at the VLT from the NACO-ISPY survey, as well as a new Y –H spectrum and K-band photometry from SPHERE-SHINE. Using these data, we confirm the nature of the companion as a warm, dusty planet with a mid-L spectral type. From comparison of its SED with the BT-Settl atmospheric models, we derive a best-fit effective temperature of T_eff = 1618 ± 7 K, surface gravity log g = 3.78_−0.03^+0.04 and radius R = 1.17 ± 0.04R_J (statistical uncertainties only). Using the DUSTY and COND isochrones we estimate a mass of 8 ± 1M_J. Combining the astrometric measurements from our new datasets and from the literature, we show the first indications of orbital motion of the companion (2.6σ significance)and derive preliminary orbital constraints. We find a highly inclined orbit (i = 1.07₋₁₀⁺¹³ deg) with an orbital period of 800₋₄₀₀⁺¹²⁰⁰ yr. We also report SPHERE sparse aperture masking observations that investigate the possibility that HIP 65426 b was scattered onto its current orbit by an additional companion at a smaller orbital separation. From this data we rule out the presence of brown dwarf companions with masses greater than 16 M_J at separations larger than 3 AU, significantly narrowing the parameter space for such a companion.