"Is cóisir áitiúil í."
Translation:It is a local party.
Like Spanish, all nouns in Irish* are either masculine or feminine. I’m unable to tell you why cóisir is feminine — there’s a theory that tries to explain the original reason for masculine/feminine/neuter gender divisions in Proto-Indo-European, but I don’t know whether that same theory would equally apply to all of the intermediate languages between Proto-Indo-European and modern Irish.
There are some noun gender patterns that apply in Irish, but it’s not always readibly discernible what the gender of a particular Irish noun is. In this case, if a noun ends with a slender consonant but doesn’t end in -ín, -éir, -eoir, -óir, or -úir (which are generally masculine endings), the odds are good that the noun is feminine.
* — With the singular exception of the noun euro (see here for details).
If you are trying to say "The party is local", you wouldn't use the cupola, because "local" is an adjective, not a noun, so you'd say Tá an cóisir áitiúil.
With "It is a local party", you are linking two nouns (actually a pronoun and a noun) "it" and "party", so you use the cupola - Is cóisir áitiúil í. For "It is the local party", you would use is í an chóisír áitiúil í.