Do the Scriptures teach, either directly or indirectly, that the NT believer is to make use of the law? Yes.
2 Tim 3:16-17
16 All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:
17 That the man of God may be perfect, throughly furnished unto all good works. (KJV)
To answer other than yes is to declare the law to be other than inspired text. Few Christians would take such a position. This requires us to conclude that the law is of SOME use to the Christian. Now we are faced with the more difficult question regarding how the Christian should make use of the law.
To make this determination we can begin by determining if, and how, indwelt Christians are instructed to consider the implications of OT law upon how they should conduct themselves.
In some cases the OT law is essentially quoted. And the clear intent is that the recipients follow the instruction provided in the Law.
Consider James NT warning . . .
James 2:8-9
8 If you really fulfill the royal law according to the Scripture, "You shall love your neighbor as yourself," you do well;
9 but if you show partiality, you commit sin, and are convicted by the law as transgressors. (NKJ)
. . . and the OT basis for that instruction.
Lev 19:15
15 Ye shall do no unrighteousness in judgment: thou shalt not respect the person of the poor, nor honour the person of the mighty: but in righteousness shalt thou judge thy neighbour.
(KJV)
Consider Peters Command . . .
1 Pet 1:15-16
15 But as he which hath called you is holy, so be ye holy in all manner of conversation;
16 Because it is written, Be ye holy; for I am holy. (KJV)
. . . and the origins of that command.
Lev 11:44
44 For I am the LORD your God: ye shall therefore sanctify yourselves, and ye shall be holy; for I am holy: neither shall ye defile yourselves with any manner of creeping thing that creepeth upon the earth. (KJV)
Lev 19:2
2 Speak unto all the congregation of the children of Israel, and say unto them, Ye shall be holy: for I the LORD your God am holy. (KJV)
Lev 20:7-8
7 Sanctify yourselves therefore, and be ye holy: for I am the LORD your God.
8 And ye shall keep my statutes, and do them: I am the LORD which sanctify you. (KJV)
And . . .
Rom 12:19
19 Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord. (KJV)
Deut 32:35
35 To me belongeth vengeance, and recompence; their foot shall slide in due time: for the day of their calamity is at hand, and the things that shall come upon them make haste. (KJV)
Paul also directly invoked the authority of one of the 10 Commandments.
Eph 6:1-3
1 Children, obey your parents in the Lord: for this is right.
2 Honour thy father and mother; (which is the first commandment with promise

3 That it may be well with thee, and thou mayest live long on the earth. (KJV)
Exod 20:12
12 Honour thy father and thy mother: that thy days may be long upon the land which the LORD thy God giveth thee. (KJV)
In each of these cases, the authority of Gods law is considered sufficient to inform the NT Believer regarding what ought or ought not to be done.
One NT author, under the inspiration of the Spirit of God, applied the OT law as case law, using it as the source of a precept having more broad application in NT days.
1 Tim 5:17-18
17 Let the elders that rule well be counted worthy of double honour, especially they who labour in the word and doctrine.
18 For the scripture saith, Thou shalt not muzzle the ox that treadeth out the corn. And, The labourer is worthy of his reward.
(KJV)
Deut 25:4
4 Thou shalt not muzzle the ox when he treadeth out the corn.
(KJV)
Again, in each case there is a direct reference to the law of God. In each case the instruction is to Christians within whom reside the Holy Ghost. And although it can be assured that the Spirit of God was a participant in the recipients ability to accept and apply the instruction, there is no direction from the NT teachers to specifically seek a Spiritual unction. Rather, direct reference is made to the law of God.
So we have seen clearly that the Law of God is, at times, treated as authoritative by the NT Authors. But is all of the Law to be treated equally? The Scriptures provide this answer as well.
Two aspects/categories of OT Law seem to have been fulfilled in Christ, bringing their purpose to fulfillment and their mandated observance to an end.
The dietary laws, along with the laws regarding particular days and dietary practices . . .
Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath [days]:
Which are a shadow of things to come; but the body [substance] [is] of Christ. (Col 2:16,17)
This would seem to clearly indicate that the laws governing food, drink, and OT observances were a picture/shadow of Christ and therefore no longer in effect while we are in Christ, (i.e., now that there purpose has been fulfilled).
The ceremonial laws regarding the sacrificial system . . .
From Heb 8
Who serve unto the example and shadow of heavenly things, as Moses was admonished of God when he was about to make the tabernacle: for, See, saith he, [that] thou make all things according to the pattern shewed to thee in the mount. But now hath he [Christ] obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises.
From Heb 9
[It was] therefore necessary that the patterns of things in the heavens should be purified with these; but the heavenly things themselves with better sacrifices than these. For Christ is not entered into the holy places made with hands, [which are] the figures of the true; but into heaven itself, now to appear in the presence of God for us:
Clearly the OT worship and sacrificial laws were intended as a precursor to, and picture of, that which was fulfilled in Christ.
This seems to be what was meant in Matt 5.17 wherein it states, Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil.
This general principle, the cessation of observing some of the OT laws, while upholding others seems to be succinctly illustrated in the following verse.
1 Cor 7:19
19 Circumcision is nothing, and uncircumcision is nothing, but the keeping of the commandments of God. (KJV)
The aggregate indicates that those laws, ceremonies, and observances that foreshadowed or otherwise pictured the Christ who would come have been fulfilled in Him and therefore, the related laws and observances themselves, abrogated.
Clearly, none of this text teaches contrary to the commands to the believer to walk after the Spirit. Neither does it challenge the clear teaching that we cannot be justified (judged to be righteous) under the light of the law, but are fully dependent upon, and trusting in, the grace of God for our salvation our right standing with Him.
Still, it is Gods law that reflects for all of the world His standard for righteousness, and we ought to be pleased and constrained to walk in obedience to it. What that means, exactly, remains a subject with which we might wrestle.