Depends on severity. The severity of aorta coarctation is defined by the pressure gradient it causes--i.e. How much it obstructs blood flow across it. If this is severe enough, surgical correction is often needed. However, sometimes interventional techniques using catheters can be used at specialized centers. Importantly, follow-up care is crucial to detect other problems that are often associated with this diagnosis.
Procedure. The general rule is that coarctation that is significant enough to cause symptoms/signs (e.g. Hypertension) will require a procedure to be corrected. Those options are either surgery or catheterization. Most can dealt with in the cath lab. Please discuss your case with your cardiologist.
Stent vs surgery. Once diagnosed other defects that are associated need to be found and treated. Berry aneurysms in the brain and bicuspid aortic vales should be looked for and treated. Other defcts like PFO and mitral valve defects should be sought. Otherwise coarctation can be treated with percutaneous ballon angioplasty, stent placement or surgically. Sugical appraoch for infants, stenting for older pts usually.