During the scene, Lara discovers that her axe needs an upgrade. You'll need to collect enough salvage to give the pry axe the upgrade it needs to move on. Use the axe on the small crates scattered around the area to obtain the salvage, then return to the gate camp to upgrade. Strengthen it through the menu, then head over to Whitman to move on. Press the prompted button repeatedly until the gate rises. Now follow Whitman up the path until the pair is interrupted by the voices of strangers, initiating a cutscene. Afterward, get behind the wall of cover to begin a segment of sneaking around. Wait until the first guard is nearly behind Lara before making your way along the next wall. Eventually, the men will notice that Lara is missing; walk past a couple of men into a nook to set off a scene.
Complete the QTE to obtain your first gun: a semi-automatic pistol. Follow a narrow path to the side, up the stairs and across the bridge, and up another set of stairs. A cutscene follows where Lara is attacked yet again. Fight back by shooting, then open the doors up ahead using the axe. Unfortunately, she's noticed, and the gate is shot with a flaming arrow in an attempt to burn her out. Follow the short QTE to escape, and move forward until you reach a split in the past. Go left and kill the man holding the flashlight up on the ledge. Scale the wall to his location, then jump up on the ledge. Move along it around the corner and climb up onto solid ground, where two more gunmen will be waiting obliviously. Get behind cover and shoot them down to move forward. Another will descend from the ladder up ahead. Shoot him down for a new objective.