Both "další" and "jiný" can mean "other/another." The difference is that the former has the sense of "additional," while the latter has the sense of ""different." Since there is no context in the English sentence, I suspect that both adjectives would be accepted.
Are jiná and další interchangeable in the Czech language? In English they are not necessarily, depending on the context. So which means "not this woman, but a different one" and which means "there are not enough participants, we need another woman"?