General assumptions: Using a keycard is one of options to get to the arena, where fights take place. Finding the card and using it are relatively simple steps, which in addition are not time consuming.
If you want to get to the next location in a traditional way, without showing up on the ring disguised as Patriot, you have to find a keycard, lost by one of the guards. In order to do it, go to the other end of the hangar, behind the trailer, where Patriot and his men are stationing. The keycard lies on the ground in a place shown on the above screen and you have to watch out, because this area, depending on the difficulty level, is patrolled by one or two guards.
Before you leave the hangar, I would suggest obtaining disguise. Once you proceed to the second stage of this mission, the most useful will be Patriot's entourage disguise, allowing you to freely explore most areas of the arena. This disguise can be easily obtained. Start with sabotaging a generator located at the back of the trailer (screen above).
Wait, until one of Patriot's men appears here and then attack him. Hide his body in the container behind your back and put on his clothes. Return now to the starting place and head to the left door shown on the above screen, unlocking them with previously found keycard.
Enter the unguarded room, climb down and use the ventilation shaft shown on the above screen. Listen to a conversation with Sanchez, learning that Victoria is being held by a sheriff in a local prison. Exit the shaft and open the door leading to the vicinity of the arena.
Note - I recommend now reading The Arena - Exploring the arena and The Arena - Murdering Sanchez in traditional way subchapters, connected with this method of behavior.