I admit that makes sense, but, again, grapple rules do not literally say (as far as I can tell) that you lose the use of any of your appendages to maintain the grapple.
Using at least one free hand, you try to seize the target by making a grapple check instead of an attack roll: a Strength (Athletics) check contested by the target's Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use). You succeed automatically if the target is incapacitated. If you succeed, you subject the target to the grappledcondition. The condition specifies the things that end it, and you can release the target whenever you like (no action required).
Like everyone else already said, other than depriving you of a hand, grappling doesn't limit your actions.
Also, any creature can make an unarmed strike using any part of their body that makes sense, so you always have an attack option even if both hands are holding something.