Can you discard any Gear the round you play it?

No, you cannot discard a Gear card after it has been played.

According to Rule 409.1, "Discarding a card is moving it from a player's hand directly into their trash." Once a Gear card is played, it is no longer in your hand; it is on the board as a Game Object (Rule 146.1.a). Because it is no longer in your hand, it is no longer a valid target for a discard action.

If you wish to move a Gear card from the board to the trash, you must use a game effect that specifically instructs you to "kill" or "destroy" the Gear (Rule 146.1.a.4), rather than discarding it.