The book of Leviticus is best known for being least known among the books of the Bible. For a book of such length and detail, it is indeed a shame to be shunned by so many a Christian.
Although believers under the New Covenant are explicitly not required to follow the requirements for worship of the Covenant of Moses (John 4:21, 23-24), there are two very important timeless requirements of worship detailed in Leviticus that remain for all believers.
First, you need a priest to sacrifice for your sin. This is what makes up all of Leviticus chapters 1 – 17, and is repeated for New Covenant believers in Hebrews 9:22 with Christ as our priest offering Himself as our sacrifice (Hebrews 7:23 – 8:1)
Second, you need to live holy. This is what the second half of Leviticus is all about. This is a common truth for Christians today, but its roots are in Leviticus. 1 Peter 1:14-16 is the go-to verse for holy living in the New Testament, and it is nothing more than a verbatim quote from Leviticus 19:2.
Just because you and I no longer stand in queues at the Temple to offer sacrifices through a priest, does not mean you and I are not in need of a sacrifice and a priest to worship God correctly. Christ is our sacrifice and our priest, and lest we glance over His great work on our behalf, the book of Leviticus is there to remind you what a great work our priest has accomplished for us.
And now, to top it off in true Leviticus vocabulary, here is Leviticus in two verses:
I appeal to you therefore, brothers, by the mercies of God, to present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship. Do not be conformed to this world, but be transformed by the renewal of your mind, that by testing you may discern what is the will of God, what is good and acceptable and perfect.