1984 Chapters 3.3
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I believe the intent is for O'Brien to look trustworthy, not so much to look old, but rather to have a fatherly appeal. His appearance, and his ability to show paternal traits such as tenderness are the things that allow him to gain Winston's trust.
Sorry, I saw this question so I thought I'd add a point. Jill no need to erase yours. In the book O'Brien knows that Winston thinks he (O'Brien) looks old. O'Brien says that Winston must wonder how the party can be perpetual if O'Brien himself is getting old and breaking down. To answer this O'Brien goes on to explain how he is merely a cell in the infinite machine of the party.