The short answer is a resounding Yes! But why we have to, for what and how?
It was established by Paul that even those who are not Jews follow the Law (Rom 2:14). Even now, there are non-Christians who believe and love their own God and their neighbors. Their “righteousness” however, is not the “righteousness of God” which are reflected through the Holy Spirit as “fruits of the Spirit”. These are the same people who will be rejected by Christ for their “own good works” (Matt 7:21-23) because they were not “works of the Holy Spirit” that God acknowledges. It is God who chooses what he likes and requires, what is acceptable to him, in spite of how good the works are.
Remember Abel and Cain? God chose Abel’s offering because it was “by faith”(Gen 4:3-5; Heb 11:4) not Cain’s. The rest of the Bible shows examples of the precept that God alone chooses what is to his liking, no matter what we think.
To start with, everything about our salvation, i.e. becoming a “new creation” members/body of the “kingdom of God”, was done not by you or me but by Jesus, the Messiah, the Logos of John 1 and the Creator Elohim in Genesis 1 & 2. It was all a gift by grace and out of love of the Father as in John 3:16. He is the “righteousness of the Law fulfilled in us” (Rom.8:4).
The death of man-Jesus (the Creator God) was substitutionary to pay the penalty of human’s sin, for mankind to be reconciled to the Father. The goal of his death is reconciliation, nothing more. Had he not been resurrected by the Father, Jesus could have died eternally and we are still “dead in sin” (I Cor 15:17). But, because of the Father’s promise of resurrection and the “faith of Jesus” in him, he was made alive. Having been resurrected to life, we “shall be saved by his life”(Rom 5:10).
Notice, the phrase “shall be saved”, meaning future, not yet, or in the process of salvation. But, how are we going to “be saved by his life”, his resurrected life? Remember Jn 16:7; 15:26; 14:16? He was resurrected for this very purpose, i.e., for the promised Holy Spirit to be sent and dwell in us, for us to “be endowed”, starting at Pentecost (Luke 24:49; Acts 1:4; Gal 3:14). We received this HS not by (our) works of the law but by “faith of Jesus” (Gal 3:2).
Why do we need the Holy Spirit? As circumcision is a “sign”, the HS serves as a “seal” to identify us being in the “body of Christ” (Jn 6:7; 2Cor.1:21-22; 5:5; EpEph 1:13-14; 4:30 Aside from that, we need “spirit-power” as the “flesh is weak”, (Matt 26:41). We need the Holy Spirit of power to be used by us to express the “fruits of the Spirit” (Gal.5:22-23). The HS gives us “cognition” as to which way to go or do, “conviction” to follow Jesus'(YHVH ELOHIM’s) Law, and “affection” for him and whatever is “good”, giving us the “mind of Christ” (I Cor 2:16).
That said, according to Paul, “the Law is holy” (Rom 7:12, v-14,v-23); nothing wrong with the Law and the Covenant. What was wrong was us, the flesh-nature that we have, that is “weak”. Remember that in Genesis, YHVH made “man (from dust) after his image”, and in the future to be “like him’. But that “clay” was flesh and “weak” so Adam could not be “like him” by his “own works”. It has to be by the “faith of Jesus”.
Adam, not knowing his “weakness”, did not “listen and follow” God, so he sinned and was banished from the “garden of Eden”. Adam was separated from God and needs to be “reconciled”. Having been reconciled by Christ’s death, we are now “being saved by his life through the function and power of the Holy Spirit” given to us as promised, to (bring many sons to glory” (Heb 2:10).
Therefore, with the power of the Holy Spirit, follow the Ten Commandments as part of our process of “sanctification” (I Cor 6:11; Rom 8:9-11; 15:15-16; 2 Cor 1:21-22; Eph 1:13-14; 2 Thes 2:13; itus 3:4-7; I Pet 1:1-2; 2:9-12; John 17:17; Rom 6:19-22; 8:5-14; Gal 5:16-24; I Pet 2:11; Rom 2:6-7).
With “eyes to see, let him see; ears to hear, let him hear” the truth.