Aims. On the Sun, jets in light bridges (LBs) are frequently observed with high-resolution instruments. The respective roles played by convection and the magnetic field in triggering such jets are not yet clear. Methods. We report a small fan-shaped jet along a LB observed by the 1.6m Goode Solar Telescope (GST) with the TiO Broadband Filter Imager (BFI), the Visible Imaging Spectrometer (VIS) in Hα, and the Near-InfraRed Imaging Spectropolarimeter (NIRIS), along with the Stokes parameters. The high spatial and temporal resolution of those instruments allowed us to analyze the features identified during the jet event. By constructing the Hα Dopplergrams, we found that the plasma is first moving upward, whereas during the second phase of the jet, the plasma is flowing back. Working with time slice diagrams, we investigated the propagation-projected speed of the fan and its bright base. Results. The fan-shaped jet developed within a few minutes, with diverging beams. At its base, a bright point was slipping along the LB and ultimately invaded the umbra of the sunspot. The Hα profiles of the bright points enhanced the intensity in the wings, similarly to the case of Ellerman bombs. Co-temporally, the extreme ultraviolet (EUV) brightenings developed at the front of the dark material jet and moved at the same speed as the fan, leading us to propose that the fan-shaped jet material compressed and heated the ambient plasma at its extremities in the corona. Conclusions. Our multi-wavelength analysis indicates that the fan-shaped jet could result from magnetic reconnection across the highly diverging field low in the chromosphere, leading to an apparent slipping motion of the jet material along the LB. However, we did not find any opposite magnetic polarity at the jet base, as would typically be expected in such a configuration. We therefore discuss other plausible physical mechanisms, based on waves and convection, that may have triggered the event.