The context is holy living. It begins with an understanding of God’s work in bringing the gospel to us (the OT prophets prophesied) and of the tremendous value of the gospel (the prophets inquired and the angels long to see). There is an extraordinary privilege to be alive this side of the cross.
v13 is the consequence of this understanding. Knowing the gospel leads to a clarity of mind (sober-minded) which is followed by placing our hope fully on the future promises in Christ. Motivation for holiness is our love for Christ (v8) but here it really hinges on seeing ourselves in the context of God’s redemptive history. We won’t be prepared for lives of loving sanctification if we can’t see where we’ve been (“former ignorance” v14) and where we’re going in Christ.