You cannot directly have one trigger then another, but there are a couple of ways that you could work around this. The workarounds depend on what your signal looks like.
If your each of your trigger lines just sends a trigger pulse then it would be more difficult, but you could have one task that looks for the trigger, then sets a line high as say the gate for the clock signal for the main task. On the main task you could have it looking for the trigger line and if the gate is high then the clock signals will come in and the acquisition will be made. If you want to do the operation once it should work.
There are a couple other possible solutions, but most are software timed and whether or not they would be effective would depend upon your acquisition rates, the amount of time between triggers, whether or not this operation needs to repeat, etc.