Cyrilavis colburnorum, an Eocene stem-parrot from the Green River Formation of USA.
While the very earliest parrots probably lived in the Paleocene, there aren't many good fossil birds from the time period. The following geological epoch, Eocene, is different. Whole bird skeletons have been preserved in Green River formation in USA and in Messel and London Clay localities in Europe - and all of them have parrots.
These stem-parrots didn't look much like their modern relatives, though. They still lacked the trademark hooked beak, and looked somewhat like a cross between a parrot and a crow - which is only logical, as passerines are the closest living relatives of parrots. A transitional fossil, in a way. Zygodactyl feet, with two digits pointing forward and two backward, are already there.
I gave Cyrilavis a colouration lacking the bright reds and greens that are familiar in today's parrots. Those are formed with psittacofulvines, a class of pigments unique to parrots that possibly had not yet evolved at this point. It might look a bit too much like a cockatiel, though. It was hard to avoid it, with four cockatiels living in the room next to this.