This Collect is in part inspired by that of the parallel prayer in the 1962 Missale Romanum. However, it seems to be a rather new creation, if not entirely new.
Deus, qui huius diei venerandam
sanctamque laetitiam in apostolorum
Petri et Pauli sollemnitate tribuisti,
da Ecclesiae tuae
eorum in omnibus sequi praeceptum,
per quos religionis sumpsit exordium.
There is a usage in late Latin of sumo and exordium which is surely at work here: "to make a beginning".
Since this seems to be a fairly new prayer we have a little flexibility with religio. It might be hard to do better than entry in the great Lewis & Short Dictionary says: "Reverence for God (the gods), the fear of God, connected with a careful pondering of divine things; piety, religion, both pure inward piety and that which is manifested in religious rites and ceremonies; hence the rites and ceremonies, as well as the entire system of religion and worship, the res divinae or sacrae, were frequently called religio or religiones". On the other hand, the source for liturigcal Latin Blaise/Dumas suggests merely: "piete" and "religion". Religio in our context needs a word or phrase that gets at the external express or our interior attitude.
VERY LITERAL VERSION:
O God, who for the solemnity of the
apostles Peter and Paul
bestowed the holy and venerable joy of this day,
grant to Your Church
to follow in all things their instruction
through whom she made a beginning of the life of faith.