Many people confuse Old/New Testament with Old/New Covenant. The Testaments usually refer to the books, and the Covenants to the deals made in those books between God and physical/spiritual Israel.
Almost all Christians believe they are part of a New Covenant with God to set an example of personal behaviour, and not part of the Old Covenant, which was intended for the physical nation of Israel to set a societal example to the world.
Some, but by no means all or even most, Christian denominations also hold the belief that the Old Testament book is no longer relevant or applicable to them.
As for Quakers (Friends), they don't consider either part of the Bible nearly as seriously as most other denominations. They view it not as a source of literal truth, but as a source of spiritual principles and ideas.
God hath seen that herein we should see as in a looking-glass the conditions and experiences of the saints of old, that finding our experiences to answer to theirs, we might be time more confirmed and comforted and our hope of obtaining the same end strengthened.... This is the great work of the Scriptures and their service to us, that we may witness them fulfilled in us, and so discern the stamp of God’s Spirit and ways upon them by the inward acquaintance we have with the same Spirit and work in our hearts.
— Robert Barclay, quoted in A Quaker Approach to the Bible - by Henry Joel Cadbury