제가 모든 팬 분들께 대신해 사과드립니다.

"나는 모든 팬분들 대신 사과드립니다" is correct but sounds a little unnatural. A better way to phrase it would be: 1. 모든 팬분들 대신(에) 제가 사과드립니다. 2. 모든 팬분들을 대신해(서) 제가 사과드리겠습니다. As with the English version, putting the subject and verb closer (제가 사과드립니다) is better. #2 suits this type of formal speech better than #1 (사과드립니다 is quite formal). -를 대신해(서) is more formal and fully phrased than the shorter form 대신, so more suitable for formal contexts. 사과드립니다 is like "I apologize; I am apologizing", 사과드리겠습니다 is "I will apologize". Both are fine. In formal speech intended for a multitude of people, 저는 is always more appropriate than 나는. Edit: Seeing Edwin's answer below, I realize my interpretation above might be wrong. "on behalf of" can mean 1. representing (대신에, 대표해서), or 2. in the interest of (-를 위해서). I took it as #1 without much thinking, but that implies "all the fans" have done something wrong to apologize for, which doesn't make much sense. So #2 is probably what you meant. If so, it should be 제가 모든 팬분들꼐 (대신/대표로) 사과드립니다, or 모든 팬분들의 이름으로 제가 대신 사과드립니다. This seems more likely, as it implies a small group have done something bad and he is apologizing as the representative of the artist to the fans. Hope this was not too confusing to you, and thanks to Edwin for catching it.