Just curious. Does the CoC dismiss the Old Testament? Thanks.
Absolutely not. The whole Bible is necessary to fully understand God's will.
2 Timothy 3:15-17
15 and how from infancy you have known the holy Scriptures, which are able to make you wise for salvation through faith in Christ Jesus. 16 All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness, 17 so that the man of God may be thoroughly equipped for every good work.
Now does the Old Covenant still bind us? No. Hebrews 8 explains this:
6 But the ministry Jesus has received is as superior to theirs as the covenant of which he is mediator is superior to the old one, and it is founded on better promises. 7 For if there had been nothing wrong with that first covenant, no place would have been sought for another. 8 But God found fault with the people and said: The time is coming, declares the Lord, when I will make a new covenant with the house of Israel and with the house of Judah. 9 It will not be like the covenant I made with their forefathers when I took them by the hand to lead them out of Egypt, because they did not remain faithful to my covenant, and I turned away from them, declares the Lord. 10 This is the covenant I will make with the house of Israel after that time, declares the Lord. I will put my laws in their minds and write them on their hearts. I will be their God, and they will be my people. 11 No longer will a man teach his neighbor, or a man his brother, saying, Know the Lord, because they will all know me, from the least of them to the greatest. 12 For I will forgive their wickedness and will remember their sins no more." 13 By calling this covenant new, he has made the first one obsolete; and what is obsolete and aging will soon disappear.
Colossians 2:14 and following (among others) shows that the Old Testament was no longer in force but that the New Covenant is.