Order Priority Card
The Order Priority Card will allow you to get the first move for the next turn. After playing an Order Priority Card, your first order will happen before your opponent's first order. After the first orders are executed, the rest of the orders will be executed normally, just as if you were selected to go first in the random that normally happens.
If multiple players play an Order Priority Card in the same turn, the move order will be determined normally (i.e. random) between those players. The players that didn't play an Order Priority Card will also be determined normally between each other, but their first order will not go before someone who played the card.
It's possible to play more than one Order Priority Card in a turn, in which case you will go before a player who plays fewer Order Priority Cards than you did. However, playing more than one when your opponent doesn't play any will not give any additional benefit over playing just one.
Since they control different mechanisms, playing an Order Priority Card and an Order Delay Card in the same turn is allowed. The Order Priority Card will help your first order to go first, and the Order Delay Card will help orders that come after it to go last.