Priests are required to receive under both species (I’m looking for a reference for that, but so far coming up empty).
From the Council of Trent Session 21, Chapter 1"
"That laymen and clerics, when not sacrifising, are not bound, of divine right, to communion under both species.
Wherefore, this holy Synod,–instructed by the Holy Spirit, who is the spirit of wisdom and of understanding, the spirit of counsel and of godliness,(f) and following the judgment(g) and usage of the Church itself,–declares and teaches, that laymen, and clerics when not consecrating,(h) are not obliged, by any divine precept, to receive the sacrament of the Eucharist under both species ; and that neither can it by any means be doubted, without injury to faith, (l) that communion under either species is sufficient for them unto salvation. For, although Christ, the Lord, in the last supper, instituted and delivered to the apostles, this venerable sacrament in the species of bread and wine; not therefore do that institution and delivery tend thereunto, that all the faithful of Church be bound, by the institution(k) of the Lord, to receive both species. But neither is it rightly gathered, from that discourse which is in the sixth of John,-however according to the various interpretations of holy Fathers and Doctors it be understood,–that the communion of both species was enjoined by the Lord : for He who said ; Except you eat the flesh of the Son of Man and drink his blood, you shall not have life in you (v. 54), also said ; He that eateth this bread shall live for ever (v. 59); and He who said, He that eateth my flesh and drinketh my blood hath everlasting life (v. 55), also said; The bread that I will give is my flesh for the life of (lie world (v. 52); and, in fine,- He who said; He that eateth my flesh and drinketh my blood, abideth in me and I in him (v. 57), said, nevertheless; He that eateth this bread shall live for ever (v. 59.) "
~The Council of Trent - Session 21~
The following link is not an official Church source, but I believe it should be helpful why the priest must receive under both kinds.
The Priest's Communion - Part 2, Chapter 4 of The Priest in Union with Christ by Garrigou-Lagrange