Can I get a free iPhone 6 repair if the screen is faulty?

I just received a replacement iPhone 6 from my carrier and the screen has thin vertical lines running down the right side of the screen. I checked my serial number on Apple.com and it says "Repairs and Service Coverage: Active."
So my question is, will I have to pay for the repair. The phone has not been dropped. It is in perfect condition

Yeah, that is why you have insurance. Just call their support line or go to the store you got the phone from and ask them about getting it repaired or getting another refurbished phone replacement ( the phone you got as a replacement is not new, its a used refurbished phone and the one you sent in to get replaced originally will now get repaired and sent out as a refurbished phone to someone else )

If it is THE phone that you bought, of course you can get a new one. If you are under your warranty, they can replace it for free as long as the screen hasn't been open or anything is wrong with it, such as water damage, in which they don't tolerate that AT ALL. If you took your phone in and they gave you this broken one, they're not gonna fix it, they don't care what is wrong with it, as long as it works and calls and texts and does the usual. You could give it a shot though and they will probably just give you a different one.