Using the Grappler feat, one can pin a grappled target. While grappling uses one of your attacks, in the rulebook pinning takes an action.
Can I, via multi-attack access to 2 attacks, use both attacks to first grapple and then pin?
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The attack action is only able to perform the grapple:
...you can use the Attack action to make a special melee attack, a grapple. If you're able to make multiple attacks with the Attack action, this attack replaces one of them.
The pin ability granted by the Grappler feat is a different action altogether:
You can use your action to try to pin a creature grappled by you.
You would have to use your Action Surge to get an extra action (or gain it from another source) to perform both in one turn:
On your turn, you can take one additional action.
"When you hit a creature with an unarmed strike or an improvised weapon on your turn, you can use a bonus action to attempt to grapple the target. " - Tavern Brawler
If you were to use this feat, you would grapple as a bonus action after making an attack action and then you could use your main action to pin. Otherwise, not possible as stated above.