I think that there might be a couple of issues in Anna's narrative in terms of belonging. I think that Tolstoy depicts Anna as someone that is seeking to belong with her own emotional state. She is content in her marriage, not seeming overtly unhappy. Yet, when she meets Vronsky, some emotional passion from an untapped reservoir emerges. This creates a sense of alienation within her, for she is forced to live a life that is wrought with emotional unhappiness and a sense of internal agony. On one level, there is a theme of seeking to "belong" to her own happiness in trying to satisfy her longing and passion for Vronsky and for happiness. The other level of belonging would the the social setting that allows such relationships outside of marriage to happen, but criticize those who act and live in such a manner. In the end, there is a certain amount of pain that Anna endures in seeking to either belong to her social setting or not endure being ostracized for her actions.
Anna, throughout the entire book, has always wanted to "belong". In the beginning it was not quite as obvious, because then she was seen as a woman who was well put together; one who seemingly did not have any troubles in the world. Once Vronsky was thrown into the picture, Anna finally realizes that she is not happy with her current husband; she does not feel she belongs with him (a huge reason being that he is 20 years older than her).