This kitten doesn't want to drink from her own bowl but seems to prefer running water, namely the waterfall of a hang on filter.
Is this safe for the kitten? The aquarium is occupied by a terrapin which is as far as I know. And if it isn't, how can I persuade her to drink from her own water bowl?
Here are the main problems in my mind:
I'd first put a lid or covering on the tank to stop the direct access that the cat already has. If this isn't possible because the filter would still be exposed, you can try training your cat not to go there.
If the cat really only likes running water you can also get it a drinking fountain (This is the first one I found online - YMMV). The cat will be able to drink from a running water source without needing to disturb the aquarium.
The cat might also like the taste of the water. Some animals are quite the connoiseurs.
My dog prefers to drink "old" water from a big basin standing outside, one cat enjoys licking up the water puddles beneath my flower pots and the other cat prefers fresh tap water.
The chemistry of tap water differs so much from aquarium water that even you could probably taste a difference. Temperature and the material of the container also influence the taste of water.
Experiment with different containers (glas, plastic and metal bowl) and fresh and tepid water. The drinking fountain mentioned by Henders is also a nice try.
They sell fountains for cats. Basically, it's a water bowl (or basin) for the cat to drink from. The bowl is hooked up to a circulating system that keeps the water flowing. This is why your cat is attracted to the aquarium. Though many cats will drink still water, it's not uncommon for individual cats to be turned off by the idea. In the wild, still water could be stagnant or impure, so your cat's instincts may be leading it to seek out moving water.
A cat fountain can be purchased at most pet stores and will run between 30 and 80 dollars, depending on how fancy you want to get. Good luck!
I looked for fountains but couldn't find any locally that were suitable. I wondered what she was being attracted to as she didn't always drink from the waterfall.
So maybe it was the large body of water, the plastic, and no interference with her whiskers. So I tried a large stainless steel pan filled with tap water. Success!
Now to stop her from jumping out the 13 floor window onto the ledge :(