"Her parrot is drunk."
Translation:Psittacus eius est ebrius.
ea is the feminine nominative and ablative singular or the neuter nominative and accusative plural. Ei is the dative singular of all genders (to him, to her, to it), and eius is the genitive singular of all genders (of him, of her, of it). Here's a link in case you needed it: https://www.thoughtco.com/latin-demonstratives-as-personal-pronouns-120054#:~:text=While%20any%20one%20of%20these,we%2C%20you%2C%20they).
Interesting. Because the verb "to be" is one of the commonest, is this a precursor of the transition of verbs to other positions, for example second spot in English after the subject and in Romance languages like French and Spanish? Does this herald the transition from SOV to SVO?
Suus, -a, -um is only used when the possessor is also the subject of the sentence. Since the subject of this sentence is parrot, you cannot use suus. Additionally, suus is an adjective and follows the gender of the noun it modifies. Since parrot is masculine, it would be suus instead of sua. The gender of suus is not based on the gender of the possessor.
Two examples for suus vs eius: She carries her (own) parrot: Psittacum suum portat. She carries her (someone else's) parrot: Psittacum eius portat (litterally: carries the parrot of his/her). The parrot is his (own) bird: Psittacus est avis sua. The parrot is his (someone's) bird: Psittacus est avis eius.