The rules on "Grappling", specifically the "Moving a Grappled Target" section of the PHB (page 195) reads:
When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you
I wondered if monsters like the death kiss (VGM page 124), that can grapple creatures within a large reach (in this case, 15 feet) can move a grappled creature from a space in its reach to another space in its reach, without dragging it. Is this possible?