I’ve just had a look at a Clarke bench mounted drill press and had a browse through the instructions. Unfortunately, as seems to be the case with a lot of hobby drill press units the morse fitting is internal in the chuck and the end of the spindle is tapered. This is a bit of a pain as you don’t have the convenience of a slot to tap the chuck out as Len describes above. If yours is this type of fitting you have to put some sort of metal spacer between the top face of the chuck and bang the chuck upwards against the spacer and the underside face of the head. Hopefully that will split the taper. As Len suggests, heat might help as well.
This is just a typical example of the arrangement:
Clarke Drill Press