Looking forward

The Old Testament has (almost) never been read at the Eucharist during the Easter season. St. Augustine of Hippo in the fourth century started this based on earlier practices by Cyril of Jerusalem.
Instead, the Hebrew Scriptures are replaced by the Acts of the Apostles. The logic is based on the practice of looking forward from the Resurrection and balances the Easter Vigil’s looking back on our salvation history. (At the Easter Vigil, we draw out the history of our salvation in one night from creation, through Abraham, through Moses, etc.)
On weekdays in the Easter season, in fact, the Acts of the Apostles are read in pretty much a continuous way, with the whole book completed by the end of the season. The Second Readings on Sundays come from I Peter, I John, and the unusual Book of Revelation, during Years A, B, and C, respectively. The Gospel readings are almost exclusively from John.
All of this is to center us on the celebration of the Resurrection and to keep us looking forward from that event into today’s time.

Why Are There No Old Testament Readings During the Easter Season? Mike Hayes, 
https://bustedhalo.com/