The following letter shows that Popes at that time granted to certain abbesses a status sometimes called “sacerdos maxima”, parallel to that of a bishop. See here!
Source: Papae Registr. VII, 12: Mon. Germ. hist. Epp. I p. 454 sq
Piae postulatio voluntatis effectu debet prosequenti compleri, quatenus et devotionis sinceritas laudabiliter enitescat et utilitas postulata vires indubitanter adsumat. Proinde quod in honore sancti Cassiani est consecratum monasterio in quo praeesse dinosceris iuxta petitionem filiorum nostrorum Dinamii atque Aurelianae, qui id religiosa devotione domui iuris sui iunctis uniisse aedificiis comprobantur, haec privilegia praevidimus indulgeri constituentes, ut obeunte ante dicti monasterii abbatissa non extranea, sed quam congregatio sibi de suis elegerit, ordinetur; quam tamen, si digna huic ministerio iudicata fuerit, eiusdem loci episcopus ordinet. In rebus autem vel dispositione eiusdem monasterii neque episcopum neque ecclesiasticorum quemquam aIiquam habere decernimus potestatem, sed ad haec sollicitudinis tuae, vel quae post te in eadem loco fuerit abbatissa, curam statuimus per omnia pertinere. Die siquidem natalis vel dedicationis monasterii suprascripti, episcopum missarum illic sacra convenit sollemnia celebrare; a quo tamen ita hoc est officium exsolvendum, ut cathedra eius nisi praedictis diebus, cum illic missarum sollemnia celebrat, non ponatur; quo discedente, simul etiam cathedra illius de eadem oratorio auferatur. Ceteris vera diebus per presbyterum, qui ab eadem episcopo fuerit deputatus, missarum officia peragantur.
Letter to the Abbess Respecta of the monastery of Cassian at Marseille
The demand of a pious wish ought to be accomplished by a consequent result, that so the benefit demanded may be validly attained, and sincerity of devotion may laudably shine forth. Accordingly to the monastery consecrated to the honour of Saint Cassian wherein you are selected to preside—in accordance with the petition of our children Dynamius and Aureliana, who are shewn, in their religious devotion, to have united it to the house in their possession by connecting the buildings—we have seen fit to allow these privileges:—We appoint that on the death of the abbess of the aforesaid monastery, not a stranger, but one whom the congregation may choose for itself from among its own members, shall be ordained; whom (provided however that she be judged worthy of this ministry) the bishops of the same place shall ordain. Further, with regard to the property and management of the same monastery, we decree that neither bishop nor any ecclesiastic shall have any power; but appoint that these things shall in all respects pertain to the charge of thy Solicitude, or of her who may be abbess in the same place after thee. If on the day of the Saint’s anniversary, or of the dedication, of the aforesaid monastery the bishop should resort thither for celebrating the sacred solemnities of mass, still his office must be so executed that his chair be not placed there, except on the aforesaid days while he is celebrating there the solemnities of mass. And when he departs, let his chair be at the same time removed from the same oratory. But on all other days let the offices of mass be performed by the presbyter whom the same bishop may appoint.
Source: The Book of Pastoral Rule and Selected Epistles of Gregory the Great, Bishop of Rome, trans. James Barmby, Nicene and Post-Nicene Fathers, Second Series, vol. 12: Leo the Great, Gregory the Great, ed. Philip Schaff, Henry Wace, Peabody, MA: Hendrickson Publishers, Inc. 1995, pp. 215-216.
Source: Registrum Epistolarum: Book 9, Ep. 7: Mon. Germ. hist. Epp. 11 p. 185 sq. Letter to Januarius bishop of Caralis in Sardinia
Quia ingredientibus monasterium convertendi gratia ulterius nulla sit testandi licentia, sed res eorum eiusdem monasterii iuris fiant, aperta legis definitione decretum est. Quod cum paene omnibus notum sit, in magna nos Gaviniae abbatissae monasterii sanctorum Gavini atque Luxurii insinuatio ammiratione perduxit, quod Syricam, monasterii sui abbatissam, postquam regendi suscepit officium, condito testamento legata quibusdam asseruit reliquisse. Et dum de sanctitatis vestrae sollicitudine queremur, cur res monasterio competentes ab aliis pertulerit pertineri, communis filius Epiphanius archipresbyter vester praesens inventus respondit memoratam abbatissam usque diem obitus sui induisse vestem monachicam noluisse, sed in vestibus, quibus loci illius utuntur presbyterae, permansisse.
Letter to Januarius bishop of Caralis in Sardinia
It has been laid down by the plain definition of the law that those who go into a monastery for the purpose of entering on monastic life are no longer at liberty to make wills, but that their property passes into possession of the same monastery. This being known to almost all, we have been greatly surprised by the notification of Gavinia, abbess of the monastery of Saints Gavinus and Luxorius, to the effect that Sirica, abbess of her monastery, after receiving the office of government, had made a will leaving certain legacies. And when we enquired of the Solicitude of your Holiness why you endured that property belonging to the monastery should be detained by others, our common son Epiphanius, your archpresbyter, being present before us, replied that the said abbess had up to the day of her death refused to wear the monastic dress, but had continued in the use of such dresses as are used by the presbyteresses of that place.
Source: Selected Epistles of Gregory the Great, Bishop of Rome, trans. James Barmby, Nicene and Post-Nicene Fathers, Second Series, vol. 13: Part II: Gregory the Great, Ephraim Syrus, Aphrahat, ed. Philip Schaff, Henry Wace, Peabody, MA: Hendrickson Publishers, Inc. 1995, p. 4.