React/TypeScript: extending a component with additional properties

You’ll need to make DataTable generic so that you’ll be able to use an interface which extends DataTableProps:

export interface AnimalTableProps extends DataTableProps {
    onClickFunction: Function;
}

export class DataTable<T extends DataTableProps> extends React.Component<T, {}> { }

export class AnimalTable extends DataTable<AnimalTableProps> {
    render() {
        // this.props.onClickFunction should be available
    }
}