"Moved on" means left a place, topic, or situation and proceeded to the next one. It can also mean emotionally recovered from a past event or relationship and started a new chapter.
For two and a half years, I rigorously trained seven to eight hours a day in two disciplines of dance but moved on to the most versatile medium called cinema which encompassed every form of art. Kamal Haasan
Laila has moved on. Because in the end she knows that's all she can do. That and hope. Khaled Hosseini
I have moved on from being a British parliamentarian, I have moved on from being a New Labour politician, I have moved on from being the supporter in the active day-to-day sense of Tony Blair. Peter Mandelson
I grew up on games like Madden and NBA Jam, then moved on to NFL 2K on Dreamcast. The game I really loved was Virtua Tennis. Chris Paul
I was still young when I missed Beijing. I was favourite to win a medal but I knew I had time. My coach advised me to stay at school and finish my exams. Even if I had gone and won the Olympics, I might not have handled the pressure. So I moved on. David Rudisha
Dad built houses and when they were sold, he moved on to a new town, so I know a lot about my native state. Gerald McRaney