Does the nasal septum grow? is it a living bone?

The nasal septum obtains it's anatomy from the overlying tissues that provide nutrients. In some operations on the septum parts of this structure can be removed or it's shape changed to improve nasal function.

The septum is composed of both bone and cartilage, and both tissues are living. For more information and diagrams, please see link below

The nasal septum has two components, the front part is composed of cartilage while the back part is bone.  The blood supply to both of these components comes, mostly, from the soft tissue that surrounds it on either side.  This soft tissue is called mucosa and is similar to the skin that surrounds our body (although, unlike skin, mucosa covers the inside of the nose and makes mucous).  During a septoplasty surgery, it is common to take out the cartilage and bone, remove the bent parts, and replace the straight parts.  This replaced cartilage and bone helps to provide support to the nose and blood vessels grow back into it from the mucosa.