I can't find my ring. Oh, there it is.
Is the word "there" an adjective in the sentence above? or is it a pronoun? For me it looks like the word "it" is the pronoun, but I'm not completely sure.
"There" is an adverb in your sentence - specifically a locative adverb or adverb of place. Example sentences include:
I need to go back to the office because I left my wallet there.
I've heard Switzerland is lovely, but I've never been there.
"Where is Bobby? There he is.
See the top definition here for more details.
Also, you are correct that "it" is the pronoun in your sentence.
"It" is indeed the pronoun. "There" in that construction is an exclamatory preposition rather than an adjective, though I agree that it feels as though it has some "adjective flavor".
There has its ordinary use as a locative, equivalent to the preposition phrase in/at that place.
The canonical structure of the sentence is "It is there". Ordinarily when a constituent in the predicate is "fronted" to the beginning of the sentence the verb is kept in the second position and the subject moves after it; this puts the subject in the "new information" position, and it receives the primary emphasis:
On the shelf were two candles.
Here comes the train.
There goes John.
But when the subject is a personal pronoun it is almost by definition "old information"—it has already been introduced into the discourse. The subject and verb remain in place.
Here it comes.
There he goes.
There it is!
THe fronted constituent in this construction is almost always here or there. The construction is typically used to announce an expected or sought-for event. If the verb is BE, as in your example, the fronted constituent gets the primary emphasis, and the sentence announces that the expected event has finally occurred:
There it is! = I've found it (at last) or It's arrived (at last).
With other verbs the primary emphasis usually falls on the verb, and the sentence announces that the expected event is finally in progress:
Here it comes. = At last! It's coming!
There he goes. = He's departing, as we expected or, figuratively And now he's doing just what we expected.