"The old lady is wearing a nice dress."
Translation:Den gamla damen har på sig en fin klänning.
In this case, it's more that äldre doesn't work that well attributively with the determinate form. Den äldre damen har på sig en klänning – I would interpret that as literally comparative (she is older than some other person previously mentioned).
About the general difference between gammal and äldre, that's a bit complex and I hope someone else will step in and provide an explanation of that, I just wanted to weigh in on this specific sentence.