When a male is speaking, he refers to his older brothers as "hyung." When a female speaks, she uses the term "oppa" (오빠). Both "hyung" and "oppa" are informal and should not be used when speaking to someone you do not know well or who is of a higher status.
There are also gender-neutral terms for older siblings, such as "gege" (누나) for an older sister and "dongsaeng" (동생) for a younger sibling.