Looks like a threaded chuck with a set screw against the threads to prevent unscrewing when the lathe is reversed. The chuck may be stuck. Do not use the back gears to lock the spindle. You may break teeth.?
If it is a threaded chuck, place the spindle in "neutral" so that the chuck and spindle turn free. Chuck up a large diameter bolt like 1/2-3/4" (12mm +) and use an impact wrench in reverse to break the chuck free.??