Asher explains to Jonas the rules regarding applying for Elsewhere in Chapter 21 of "The Giver." He says that an individual can apply for release if he or she is "very old, or very hurt, or very tired," or if they have committed a serious breach of rules. However, he adds that "nobody applies for release very often."
Jonas is uninterested in applying for Elsewhere because he has discovered the truth about the community's practice of "releasing" individuals, which is actually a euphemism for killing them. He has also learned that Gabriel, the baby he has been caring for, is scheduled for release, and he knows he cannot allow that to happen.
Textual evidence to support this can be found in Chapter 21, when Jonas tells Asher that he doesn't want to apply for Elsewhere: "Jonas shook his head. 'No. I don't want to do that. I don't want to be released.'" Jonas then explains that he knows what release really means, and that he is planning to take Gabriel and escape from the community.