A New Testament scripture that parallels Leviticus 1, which discusses the offerings and sacrifices, is found in the book of Hebrews. Specifically, Hebrews 10:1-4 addresses the concept of sacrifices and how the Old Testament sacrificial system served as a shadow of the ultimate sacrifice of Christ.
Hebrews 10:1-4 (NIV) states:
"The law is only a shadow of the good things that are coming—not the realities themselves. For this reason, it can never, by the same sacrifices repeated endlessly year after year, make perfect those who draw near to worship. Otherwise, would they not have stopped being offered? For the worshipers would have been cleansed once for all, and would no longer have felt guilty for their sins. But those sacrifices are an annual reminder of sins. It is impossible for the blood of bulls and goats to take away sins."
This passage illustrates the significance of the Old Testament sacrifices while pointing to Christ as the ultimate fulfillment of those offerings.