Yes it is. You can use either variables to do it, or you have a script elsewhere running that will destroy the particular trigger.
Here's an example...
I have an outdoor level. The player is to collect a map in a room and proceed to navigate a mine. If they do not pick up the map, they will have a hud come up part way through telling them they need the map. If they have the map, the hud does not show and that trigger is destroyed. I used the variable method for this example. When the player picks up the map, a global variable #1 is set to the value of 1. When they reach that trigger, the script in the trigger runs and checks that global variable when the player is in the zone. If the value of the variable equals 1, it destroys; if not, the hud appears and the player must return for the map. I also have it looping back to check again just in case the player thinks they can bypass getting the map.
Another example not using variables...
I can set the map entity's script to set target to the name of the trigger, then activate that target. The trigger's main script is running and checking to see if it has been activated in the beginning states. If it is not activated, it waits for about 1 second, then returns to check again. If it has been activated, I give the "state=<number>:destroy" which destroys the trigger.
There are a few other methods, but those are the common two I use myself. A bit of scripting knowledge, but it uses the basic commands available.
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