A controlled mount cannot grapple
A grapple is a "special melee attack", it is a part of the Attack action. A controlled PC mount, despite being a wolf, cannot attack. It has only Dash, Disengage, and Dodge actions, see PH page 198 "Mounted combat":
It moves as you direct it, and it has only three action options: Dash, Disengage, and Dodge.
It can if it acts independently, but it still needs a free hand
Technically speaking, you can't give an order to grapple. But a mount can do things on its own. See PH "Controlling a mount":
While you're mounted, you have two options. You
can either control the mount or allow it to act
independently. Intelligent creatures, such as dragons,
The wolf still isn't eligible though, since it have to use a free hand, see PH page 195 "Grappling":
The target of your grapple must be no more than one
size larger than you, and it must be within your reach.
Using at least one free hand, you try to seize the target
A wolf has no hands and it has no actions in its stats block, allowing it to grapple without hands. Compare that with a Giant Octopus tentacle attack, explicitly saying:
Tentacles. Melee Weapon Attack: +5 to hit, reach 15 ft., one target. Hit: 10 (2d6 + 3) bludgeoning damage. If the target is a creature, it is grappled (escape DC 16)