Renee was seen in the Processing Center, helping the new DHARMA recruits of 1973. She was seen walking around in the background, behind young Ben and Annie.
She may have been killed along with other members of the DHARMA Initiative in the Purge, or she may have left the island sometime between 1973 and The Purge.
The actress who portrayed Renee, Alice Forsyth, also portrayed other DHARMA members, including Alice and Fern.
Renee's name was labeled on her jumpsuit, which was seen in "The Man Behind the Curtain", but it's too far and blurry to identify. Fortunately, the jumpsuit was auctioned online years later, and the details were revealed.