There are a few ways:
Try using the Direction-Distance point construction tool:
With point snapping turned on, Create Features pane > Any point layer > Point tool > on the toolbar that appears on the map, choose the Direction Distance construction tool > Snap to the existing point while setting the direction and distance.
Another way, use the Point At End Of Line tool while snapping to the existing point:
Constrain the temporary line segment to a specific length by setting a Distance constraint: