6-7 hours under general anesthesia! Is this safe?

It is safe to have a long anaesthetic if necessary.  A typical Rhinoplasty takes about 90 minutes. Even with rib cartilage harvesting yours seems like a very long procedure. Clarify with your surgeon to make sure you have the numbers correct.

6-7 hours under general anesthesia, if you are healthy, is not unusual. Typically, if you have any medical issues, a pre-operative physical would be performed to ensure that general anesthesia is low risk. However, that is alot of operative time for a rhinoplasty with rib graft. There might be something specific about your nose that requires such a long operation but this is very unusual. I hope this information is helpful for you.Stephen Weber MD, FACSDenver Facial Plastic Surgeon

Six to seven hours is not an abnormally long time to be under general anesthesia, but the safety of this depends on your overall health.  Your surgeon and anesthesiologist should evaluate you before your surgery to determine if it is safe for you to undergo the procedure for this length of time or not.  

Long anesthetic times are frequently needed in complex plastic surgery cases or in combined cases.  In a healthy patient, this is usually tolerated well.  Make sure risks of VTE (venous thromboembolism) are assessed and precautions taken.

7 hours is unusually long for a rhinoplasty procedure. Most rhinoplasty procedures take approximately an  Hour and a half  under a general anesthetic. There is no reason to harvest rib cartilage unless the  the nasal septum has been depleted of cartilage from prior surgery and cartilage grafting techniques are necessary. Ear cartilage can also be used as an alternative before going to the rib. Also important to make sure you're been placed under anesthesia by a board-certified physician anesthesiologist

Modern anaesthesia is very safe as long as you are fit and healthy and are in an accredited hospital, your risks should be very low. You should discuss your concerns with your anaesthetist as they would be the best person to talk to regarding your anaesthetic. 

It is normal to be concerned with the safety of elective procedures.  Do your homework regarding the experience and qualification of your surgeon, anesthesia providers and the operating facility.  You will want to know if they are prepared to handle anesthetic and medical emergencies, such as cardiac arrest, while you are under anesthesia. For some surgeons, it is not unusual for their nasal procedures to routinely take 6-7 hours.

I think you are right to be concerned, but if you are young and healthy it is probably not too big a risk. I'd be more worried about why that operation is estimated to take that long. It shouldn't.