At 52, we can't really call David old, but we can definitely say that he feels age creeping up on him. David notices this initially when he doesn't attract the same kind of female attention that he used to receive. David seems to try to fight off old age through his relationship with Melanie – her youth appeals to him, and she reawakens feelings that he hasn't experienced in quite a while. Nevertheless, over time his perspective towards aging becomes more complex. Even at the end of Disgrace, he thinks about how being a grandfather is going to seriously damage his romantic prospects, so we can't say he totally gets over it. Still, he starts to think carefully about age during the events of the novel. He adjusts the focus of his opera to an older, more subdued Teresa rather than the young, vibrant one he previously intended to make his heroine. He stops living quite as recklessly and, whether he wants to or not, he starts to make more of an effort to care for Lucy. We see a more thoughtful David emerge as he considers the role that aging plays in his own life.
By the end of the novel, David accepts the fact that he's getting older.
David doesn't accept old age, but he accepts the role that is being carved out for him.