I would give this child some extra attention. Is there anyone that her age group teacher can pair her up with? Introduce them and get them going on doing something together. Then the older child can just go to her area. If she can't do it due to school policy, then I would go ahead and enforce the policy now. but when it is done, she is given lots of extra attention, praise from the teacher. Helping her along in making her friends if necessary. It should work out fine. If not, then the parent probably should know that the younger may need a different program than what your school offers. You don't say the age of the kids which would help.
At the preschool and elementary school I've worked at, when a child has trouble separating, we've found that a quick goodbye is best. Parents drop off and no one walks the child to class. If the parent walks the child to class, the child then becomes upset. They do much better going on their own. So, maybe the siblings need to separate outside the school and the younger child being on her own to get to her classroom. While that seems like a big deal, if done quickly, then the separation is brief. She'll get over it sooner than long goodbyes to sister.
good luck
I actually spoke to the parent about the situation and when I did the parent shrugged it off and says this is common for him to do. She says he is shy, but we have several children in the program with siblings and I have never seen a child literally not let go of his sister. I refuse to pry him off because I do not want to make a bad experience out of the situation... before he left the program the other day I had both him and his sister together at a table and I talked to them both (because he is shy and won't talk unless he is mumbling) about things they like he seemed like as I talked to him he warmed up and began to smile and nod back, but would not talk. I would try to sit down and have more one on one with him and his sister to warm him up but I can't do that because then it takes away from the attention from my group of children.
I think that the first thing that you need to do is find out why this behavior is occurring. You might need to contact the child's parents for more information on this issue as well as to report the problems you are encountering. Without knowing the exact reason for this behavior, it is difficult to advise you on an intervention other than drawing him to fun activities within the program.