The grappling rule (PH, 195) was written for a grappler with at least one hand, but a DM can easily adapt the rule for a handless creature that has a bite or an appendage, such as a tentacle, that could reasonably seize someone. A wolf, for example, could plausibly try to seize a person with its bite, and the animal wouldn’t be able to use its bite attack as long as it held onto the person.
Keep in mind that the grappling rule in the Player’s Handbook requires the Attack action, so a creature must take that action-rather than Multiattack or another action in the creature’s stat block-when it uses that rule. A monster, such as a roper, that has a special grappling attack doesn’t follow that rule when using its special attack.