I need to snap the points to the lines in another layer in order to create another line shapefile.
Is there any plugin / tool available for this? The Snap geometries doesn't take points as a reference layer.
An option would be to look into the SAGA Tools in the
Processing Toolbox. There is a Snap Points to Lines tool, which should accomplish what you are looking for. You can search for it in the Processing Toolbox by typing "Snap" or navigating:
SAGA -> Vector Point Tools -> Snap points to lines
It allows you to define the input points layer, a search distance and whether the output is in memory or a new shapefile layer.