Wanting to grow out moustache to cover scar on upper lip. Will hair grow where there's a scar? (Photos)

If you have scar the cancers are you will regrow hair in that area. Doing hair transplant done by an experinced doctor is a good option to cover the scar area. 

These scars, persisting for a year, are permanent. They can be treated in two ways (1) hair transplanted into the scar and (2) scalp micropigmentationi can work nicely, but although it will make the scar disappear, it is not hair so you can only use it if you do not grow out your mustache