Summarising this post by Jason De Rouchie:-

1. The Old Testament (OT) was the Bible of Jesus and the apostles, Mt 5:17; Lk 24:44; Acts 24:14; 2 Tim 3:15.
2. The OT shapes our understanding of key biblical truths.  It includes many promises whose fulfilment is recorded in the New Testament (NT).  It is key to our understanding of, for example, creation (Gen 1:1-2:3) and of substitutionary atonement (Isa 53).  The NT repeatedly explains itself by means of references to the OT.
3. The God of the NT is the God of the OT; Heb 1:1f.  Contrary to the prejudices of some, the OT has much to say about God’s love and compassion (Ex 34:6; 2 King 13:23; 2 Chron 30:9; Neh 9:30f), while the NT has much to say about his wrath and judgment (Mt 10:28; Mt 18:6; Rom 12:9; Heb 10:26f).  In Acts 10:42f, the apostle Peter ‘identifies himself as a proclaimer of Jesus as judge, whereas he says the OT prophets proclaimed Jesus as the means of forgiveness.’
4. The OT announces the gospel.  See, for example, Isa 61:1, comparing this with Lk 4:16-21.  See also Gal 3:8; Rom 1:1-3, 16; Heb 4:2.
5. The OT, like the NT, gives priority to love, Deut 6:5; 10:19; 30:6.  This is reaffirmed by Jesus, Mt 7:12; 22:37-40.  See also Paul’s teaching in Gal 5:14.
6. Jesus did not come to destroy the law and the prophets, but to fulfil them, Mt 5:17-19.
7. The entire OT points to Jesus, John 1:45; 5:39; Lk 24:27, 53; Acts 26:22f.
8. We do disservice both to God and to others if we fail to declare the whole counsel of God, Acts 20:26f.
9. The OT is a gift from God to those who belong to his Son Jesus Christ, 1 Pet 1:12; Rom 15:4; 1 Cor 10:11; 2 Tim 3:15-17.  The NT authors assume the relevance of the OT, 1 Cor. 9:8–12; Eph 6:2–3; 1 Tim 5:18; 1 Pet 1:14–16).
10. Church leaders are commanded to preach the OT, 2 Tim 3:15f; 4:2-4.