Well that is typically the case. Look through new Testament. The old testament scriptures are quoted when they are fulfilled or apply.
1 Peter 2:4-8
The Living Stone and a Chosen People
4 As you come to him, the living Stone—rejected by humans but chosen by God and precious to him— 5 you also, like living stones, are being built into a spiritual house[
a] to be a holy priesthood, offering spiritual sacrifices acceptable to God through Jesus Christ. 6 For in Scripture it says:
“See, I lay a stone in Zion,
a chosen and precious cornerstone,
and the one who trusts in him
will never be put to shame.”[
b]
7 Now to you who believe, this stone is precious. But to those who do not believe,
“The stone the builders rejected
has become the cornerstone,”[
c]
8 and,
“A stone that causes people to stumble
and a rock that makes them fall.”[
d]
They stumble because they disobey the message—which is also what they were destined for.
Matthew 1:22-23
English Standard Version
22 All this took place to fulfill what the Lord had spoken by the prophet:
23 “Behold, the virgin shall conceive and bear a son,
and they shall call his name Immanuel”
(which means, God with us).