In "Another class of animals is fish.", is is correct. The subject noun is class, which is singular. This is also shown in the use of another, with the an- prefix being the singular indefinite article. If the topic of animal groups or classes were already known from preceding sentences, it could also be written as:
Another class is fish.
Here it is clearer that we are discussing the class, which is clearly written in the singular form. What may be a little confusing is that fish is written the same for both the singular and plural forms. If another group were chosen, for example:
Another class is reptiles.
Reptiles is clearly written in the plural form and with some repetition we can construct the picture that the starting phrase is Another class is ...
So in this sentence, is is correct, but how it should be written is:
Another class of animal is fish.
Animal should be singular. Just as if they had written Another type of reptile is ... You can test this by replacing class with a synonym: "Another type of animal is fish." and then inverting the sentence to form a question: "Is fish another type of animal?" Here you can see that, "Is fish another type of animals?" isn't right.
Just as a point of interest, fish are not, scientifically speaking, a class of animal, but belong to one of three classes:
- Class Agnatha (jawless fish)
- Class Chondrichthyes (cartilaginous fish)
- Class Osteichthyes (bony fish)