General Anesthesia after hair transplant - how long should I wait before having another surgery involving general anesthesia?

You may have an operation under   general  anesthesia 3 weeks after the hair transplant surgery  . İt is unlike to cause any  harm to  grfats after 2-3 weeks .  General  anesthesia does not cause a serious hair loss. 

Hair loss from general anesthesia is very rare.  It is thought to be related to decrease in blood flow to the scalp for an extended period of time.   Perfusion to the scalp can decrease under anesthesia if blood pressure is low and/or if the scalp under some external pressure, like padding to hold the head in position.  In some surgeries, like spine surgery, you are face-down and there could be a fair bit of pressure exerted on the front hairline, which could involve the grafted area.   
For the first few weeks after a hair transplant the blood supply to the new grafts is still developing.  In theory, hair grafts may be at higher risk of injury from low blood flow during this time.   To be conservative, you could wait 6 weeks, at which time normal blood supply to your grafts has been established.