The whole context shows that the author of Hebrews is not asking the dead to pray for them, but instead those believing Hebrews that he can be restored to them sooner.
18 Pray for us: for we trust we have a good conscience, in all things willing to live honestly. 19 But I beseech you the rather to do this, that I may be restored to you the sooner. 20 Now the God of peace, that brought again from the dead our Lord Jesus, that great shepherd of the sheep, through the blood of the everlasting covenant, 21 Make you perfect in every good work to do his will, working in you that which is wellpleasing in his sight, through Jesus Christ; to whom be glory for ever and ever. Amen. Hebrews 13:18-21
1 Timothy 2:5 states that there is only one mediator between men and God, and that one is Jesus Christ.
For there is one God, and one mediator between God and men, the man Christ Jesus 1 Timothy 2:5
Also Jesus lives forever to intercede for us to God the Father. He is not a sinful man in the position of offering sacrifices daily to redeem us to God, for he himself is the one and only sacrifice that was offered once for our salvation, and he continues to intercede.
22 By so much was Jesus made a surety of a better testament. 23 And they truly were many priests, because they were not suffered to continue by reason of death: 24 But this man, because he continueth ever, hath an unchangeable priesthood. 25 Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them. 26 For such an high priest became us, who is holy, harmless, undefiled, separate from sinners, and made higher than the heavens; 27 Who needeth not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people's: for this he did once, when he offered up himself. 28 For the law maketh men high priests which have infirmity; but the word of the oath, which was since the law, maketh the Son, who is consecrated for evermore. Hebrews 7:22-28
Jesus tells us in the gospel of John that whatever we ask in Jesus name will be done, that God will be glorified by the Son.
12 Verily, verily, I say unto you, He that believeth on me, the works that I do shall he do also; and greater works than these shall he do; because I go unto my Father. 13 And whatsoever ye shall ask in my name, that will I do, that the Father may be glorified in the Son. 14 If ye shall ask any thing in my name, I will do it.
John 14:12-14
If Jesus is our mediator, who intercedes for us, and who will give whatever we ask in His name; why would we even want to pray to a believer who has died and awaits the resurrection?
James writes that prayer is important for those afflicted and those that are sick. He writes that the effectual fervent prayer of a righteous man accomplishes much. James does not teach that one should pray to the dead; no, he instead recognizes that believers pray to God.
He also writes that believers should confess their faults to one another, and to pray for one another.
13 Is any among you afflicted? let him pray. Is any merry? let him sing psalms. 14 Is any sick among you? let him call for the elders of the church; and let them pray over him, anointing him with oil in the name of the Lord: 15 And the prayer of faith shall save the sick, and the Lord shall raise him up; and if he have committed sins, they shall be forgiven him. 16 Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much. 17 Elias was a man subject to like passions as we are, and he prayed earnestly that it might not rain: and it rained not on the earth by the space of three years and six months. 18 And he prayed again, and the heaven gave rain, and the earth brought forth her fruit. 19 Brethren, if any of you do err from the truth, and one convert him; 20 Let him know, that he which converteth the sinner from the error of his way shall save a soul from death, and shall hide a multitude of sins. James 5:13-20
Paul writes that believers should not care (worry) for nothing, but instead pray with thanksgiving to God for all requests. Then the peace of God shall keep believers hearts and minds through Jesus Christ.
6 Be careful for nothing; but in every thing by prayer and supplication with thanksgiving let your requests be made known unto God. 7 And the peace of God, which passeth all understanding, shall keep your hearts and minds through Christ Jesus. Philippians 4:6-7