After climbing up into the corner room beyond the left side of the bridge...

...you'll see this switch...

...which opens this gate down below. The gate only stays open for 15 seconds.

Save the game here just in case. Then pull the switch.

A brief cutscene shows the gate opening, alerting a guard in that room.

Don't wait for the cutaway to end. Just press Look to get Lara's perspective back. Then roll...

...and run/slide down to the opening on the left.

Slide down the left side of the ramp and jump the gap to land on the bridge. (Or, if you slide down the middle or right side of the ramp, jump and hold Action to lower Lara's arc a bit so she doesn't bang her head on the archway.)

Turn left and run through the open gate.

Then kill the guard inside.

[Return to the Highland Fling Walkthrough]