Three examples to answer the OP come to mind.
OP: Do the rest of the Greek scriptures contain any totally new Christian doctrines not already mentioned in the Gospels or Hebrew scriptures?
The application or identification of the priesthood of Melchizedek is introduced after the Gospel accounts.
We know of Melchizedek priesthood from Gen 14:18 and Psalm 110:4, but the application to Christ is revealed in the book of Hebrews.
Called of God an high priest after the order of Melchisedec. Heb 5:10
This doctrine is explained further in Hebrews. And of course, it also leads to the priesthood of all believers, which is another new doctrine, as opposed to a blood or other lineage requirement. Here's Peter.
But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light: 1 Peter 2:9
Another new doctrine is "absent from the body, present with the Lord". Before Christ's ascension, the idea of a "holding tank" aka Abraham's bosom was prevalent. Some continue to believe in purgatory to fulfill the pre-Christ view.
We are confident, I say, and willing rather to be absent from the body, and to be present with the Lord. 2 Cor 5:8
After Christ, believers are present with Christ.
Lastly, at least for this post, is the doctrine of being righteous without having done something to earn it.
But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us. Romans 5:8
Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved;) For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Eph 2:5, 8
So, Christ made these new doctrines of a believer's priesthood, a believer's status in death, and a believer's status in life possible.