What part of speech is 'another'?

'Another' is an adjective.

At the very least, "another" is an adjective in the example you gave. In this case it is modifying "direction," a noun. By the same token, "other" is also an ajective, as in: "The people were asked to go in the other direction." The real question becomes: is "another" that very special kind of adjective we call an article?

In traditional grammar 'another' belonged to a subclass of the category adjective. But in modern grammar, it is categorized as a determinative. It derives historically from the compounding of the indefinite article 'an' and the adjective 'other'.

'Another' has alternative and additive senses: alternative as in 'go in another direction' meaning 'go in an alternative direction, and addit

thanks!

While "another" can be used as an adjective...it is also at times used as a "pronoun."

For example, "Bartender, please bring me another."