Grammar
다른 한 N
another one of several
Form
다른 한 + countable noun — “another one”, singling out one individual.
Function
Combines “different” and “one” to single out an additional member; 한 does not mean “only” here.
Why this form?
다른 N — “other / another”: does not necessarily single out exactly one member.
Forms not to confuse
다른 N
다른 사람이 왔어요. — Another person arrived.
Examples
다른 한 사람은 그보다 조금 더 어려 보인다. — The other man looks a little younger than him.
다른 한 학생이 손을 들었어요. — Another student raised a hand.