It really depends on how accurate and repeatedly accurate you want the AR carbine to become.
Thoughts:
1. Match grade ammo in the rifle you already have may get you where you want to go.
2. If your barrel is not free floated, do that next and retest.
3. If you have a mil spec trigger, you need it to be smooth and grit free. Fix that.
4. Address optics. What distance will you be shooting? If it’s a single purpose precision rifle, go for higher magnification and the best glass you can afford. If it is a multi-purpose but very accurate build (Recce or SPR) consider a scope in the 2-12x range, maybe just a classic good 3-9x.
If you are still seeking more accuracy:
A. Get the best match barrel you can afford. On the top end, accuracy and price tend to go together. If you are serious about getting down to not merely sub MOA, but sub 1/2 MOA, look to Kreiger, Lilja, Bartlein and such. My carbine to precision rifle build is based on a 16” Lilja Navy Recce barrel.
B. Get a much better match trigger, either a lighter two stage or a true target trigger. My choice is a Geissele SSA-E. The second stage is 1.2 “right now” pounds. Match triggers can be much lighter, but the resultant build might not be safe for any use except at bench.
C. Optimize the ammo to your barrel. Every barrel has preferences. If you don’t handload, try small quantities of match ammo from different companies and find what shoots best.