Yes, there is an extra cost for adding a class to your trademark registration application. Classes of goods and services define the areas where your brand will be protected (think Clothes, Perfumes, Entertainment services, etc.), and more classes equal broader legal protection.
It's important to note a higher number of classes doesn't just influence the price. When assessing your trademark, the examiner will look into your selection and determine whether, given the goods/services your brand offers, you have the right to seek protection under each of the classes. More classes also mean a higher chance of a third party opposing you if they believe you are infringing on their existing trademark in one of the classes.
Regarding fees, additional classes tend to cost less than the initial class, but the exact pricing structure depends on the country.
A few jurisdictions use a so-called "single class" filing system, where adding another class requires filing another application.
If you are not sure how many or which classes of goods and services are suitable for you, you can use our Class Assist. Alternatively, we offer a free lawyer's check where our lawyers recommend classes based on your business description.