It can go both ways. Sometimes people negotiate for a job out of residency and work a fellowship into the deal. Other times (more commonly), you'll be looking for a job after fellowship.
Most of the time you'll have to look for a job. Some places like to hang onto their better fellows, but no way they'd ever accommodate everyone, nor do they often want to. Others would rather bring back their better former residents who went elsewhere for fellowship. In general expect to be looking for at least one more job after fellowship.