"The" is a definite article, as you said, and it is a determiner— a word or phrase that precedes a noun or noun phrase and serves to express its reference in the context. In many contexts, the presence of some determiner, such as "the," is required in order to form a complete noun phrase.
The definite article "the" is used when the referent of the noun phrase is assumed to be unique or known from the context. The definite article is not used with generic nouns (plural or uncountable, I mean) or with proper nouns.
Basically, the second sentence you wrote is correct because "authority" is neither plural here, nor is authority something you can count, nor is it a proper noun. Saying that somebody "has authority to change..." is like saying "the cat has ball of yarn to play with."
Now, that sounds wrong instantly because "ball" is a familiar, simple noun, which we know is not plural, countable, or proper.
I hope this helped.