General assumptions: Using Patriot's clothes is one of options of getting to the arena. This option will result in meeting Sanchez on the ring in the next stage of mission. Elimination of Patriot in order to obtain his disguise may initially seem difficult but fortunately, in fact, it is not complicated process.
If you want to get to the next location disguised as Patriot, so you can fight with Sanchez in the ring, you have first to obtain the proper disguise. Place yourself at covers right from the trailer, where Patriot is training. Turn right (screen above) and throw any object ahead.
A falling object should lure out one of Patriot's men. Wait, until this character goes to secluded place and then attack him and hide his body in the container.
Repeat actions described above: thrown any object and hide behind crates near the trailer. This time your actions should distract Patriot himself (screen above). Notice - if the plan didn't work then stun another regular enemy and try again after hiding his body.
Same as with "regular" enemy, it would be best to wait, until Patriot goes to some secluded place. Stun or kill him, hide his body and wear The Patriot disguise.
Now return to the starting place and approach the right door shown on the above screen. Knock and wait until you are allowed to get inside.
Note - I recommend now reading The Arena - Fighting with Sanchez on the ring subchapter, connected with this method of behavior.