She must be quite thirsty and it is very important to figure out why.
It's good that you are attentive and noticed the problem.
Temperatures and humidity will both affect how thirsty a cham gets.
There is a great deal of good info here
https://www.chameleonforums.com/care/water/
Sometimes, we don't realize that more things have changed than just the new cage size.
If the room temps are warmer, she may be too hot. If the AC is running, it dries the air out and she may be in need of more water and humidity because of that.
If her cage was moved to a different location, there may be something bothering her there--like too much activity or another pet or light streaming through a closed window making it too hot.
All chams are different and maybe Zoe just doesn't like the dripper or it isn't dripping quickly enough for her to notice the water.
If she has been moved to a larger screen cage, then the same amount of misting time that she had in the smaller cage may not be making the enclosure humid enough.
Increasing the length of mistings and the frequency of mistings may be the solution.
You can add plants to help retain humidity and provide more surfaces to drink from.
You didn't say what kind of cham Zoe is, but you'll want to be sure that the temperatures and humidity are where they need to be for her.
The forum caresheets in the Resources section provide that ibfo and much more useful info
https://www.chameleonforums.com/care/caresheets/