Yes, a citizen can apply to leave the community in The Giver. You can find evidence that this is possible a page or two before the end of Chapter 6 (I have this book on Kindle and cannot give you a page number).
At the end of Chapter 6, there is a lunch break at the day of ceremonies marking the passage of children from one age to another. Jonas and Asher are talking. They are apprehensive about the jobs to which they will be assigned and Asher is telling Jonas a story about someone who was supposedly assigned to a job that he hated so much that he swam across the river and left the community. Jonas tells him this story is not true. Asher goes on to say that it is possible, however, to apply to leave. He says
If you don't fit in, you can apply for Elsewhere and be released.
This shows that it is possible to apply to leave. If you do, you will be released. As you continue to read in this book, you will find out what it means to be released in this community.