What does getting broken elbow mean in the long run?

Depends. Witout knowing more about the fracture, long term consequences cannot be predicted. Some elbow fractures will heal and after rehab will have no long-rem problems. Others, especially those with significant joint damage cause loss of motion and possible post-traumatic arthrosis. You should did the fracture with your physician.
Fracture elbow. If the elbow break is not healed, you will have pain and the possibility of damaging the area future. Sometimes if the fracture involves a joint, although the area may be healed, there is a possibility of arthritis in the future. It is very important for full range of motion to get a fracture casted or if necessary surgically repaired. If this is not done, you will have limited range of motion.
It depends. Not all elbow fractures are the same. Some, like minimally displaced radial head fractures, heal very well. Others, like olecranon fractures generally require surgery but have good outcomes. Unfortunately, there are some elbow fractures that are bad actors. This means that even with perfect care they can result in long term stiffness and dysfunction.
Elbow Fracture. An elbow fracture is either located in the distal humerus or proximal radius and/or ulna. The main concern is whether the fracture is displaced or nondisplaced. All nondisplaced fractures and those minimally displaced can be treated conservatively. Surgery is needed for the rest in order to maintain the integrity of the joint.