Ring was a female cenobite that was considered for either Hellraiser: Deader or Hellraiser: Hellworld, much like Raven, Spike and The Siamese Twins. None of these cenobites made it in the final cuts of the films, most likely due to budget cuts.
Unlike Raven, Ring's past had also been considered. Ring was apparently to be a woman who was married six times atleast, being married so many times because she became a black widow, killing her Husbands for their money or other luxuries.
Ring was to be the homeage to The Female Cenobite, which would have meant that the two knew each other somehow and The Female somehow earned Ring's respect. Her appearence is completely unknown, although, from her name, it is suggested that rings were involved in some way.