In the given figure, the galvanometer will not have a deflection if:
the bar magnet is kept stationary
An emf would be induced in the coil if there is a change in the magnetic flux. This can happen if the bar magnet and the coil move relative to each other i.e. if the bar magnet moves towards/away from the coil or the coil moves towards/away from the bar magnet. But if neither the bar magnet nor the coil moves then the induced current is zero.