to leave the place where you are staying and go somewhere else:
I've lived in this town long enough - it's time to move on.
to start a new activity:
I'd done the same job for years and felt it was time to move on.
to accept that a situation has changed and be ready to deal with new experiences:
Since he and his girlfriend broke up, he's been finding it difficult to move on.
(Cambridge Advanced Learner's Dictionary & Thesaurus からの move on の定義 © Cambridge University Press)
to start a new activity or job, especially after you have spent a long time doing a previous activity or job:
I am excited about the company's future but it is time for me to move on.
to start to discuss a new subject during a formal meeting:
Before moving on, does anyone have any questions they would like to ask?
(Cambridge ビジネス英語辞典 からの move on の定義 © Cambridge University Press)
- Cambridge Dictionary