I am not really qualified to respond to your post because I am on here as an abuse survivor myself and did not have the refuge of loving grandparents. Nevertheless, I will share my thoughts with you for whatever they are worth.

It sounds like you are providing your granddaughter with a safe, accepting and respectful environment in which to heal. Thank you for that - it is heartwarming to see. If you want to know if there's anything else you can do, why don't you ask her? It might also be a good idea to let her know, explicitly, what good things she brings to your life, because survivors often have very low self-esteem and can't imagine that they bring anything positive into the world.

As for the issue of self harm, it's probably something she has to work out for herself, but if I were you I would ask her to make a solemn promise to let you know if she ever seriously considers taking her own life. And make it clear how devastating that would be for you. She needs to know that it can't be an option, not without causing you extreme harm, which I'm sure she would not want to do.

I echo what Donna has said.
you are giving her the right envirnoment and in her time maybe she will respond.
it's hard to trust and she might be use to doing it all on her own.
ask her what she needs.

Thank you both so much, it is reassuring to know we are doing the right thing by giving her space. She is doing so well I will be sure to tell her how much she means to us both.

When I ask her what she needs she clams up and shrugs or says 'dont know'.

Something else she is finding very difficult at the moment is being away from me. I understand her anxiety, but she will be going to school soon and much as I want to be there for her, I cannot always be around.

Hello,I also have a daughter who self harms and is also attached to me.Is she in therapy?

maybe that is her truth. maybe she doesn't really know because she's never had someone there without a consequence. maybe you can talk and help her figure out what she needs.
when she says I don't know you can ask her leading questions like do you want a hug? do you want me to sit here? do you want to walk? it'll be hard for her to accept anything but the one time she does she will see she's safe and that'll be the crack in the wall you've been looking for.

She is not in therapy yet, though she will be going to a special school where they incorporate therapy into their curriculum. She has so far been resistant to the idea.
She finds it difficult to talk and doesn't speak very much, though she is a gifted writer and will write notes for me to read on her tablet.
Thank you Dash, for your helpful advice. I know we will get through in the end, it is just finding the right approach that works for her.

I'm guessing part of what she has been thru is sexual abuse since you posted here. There's another group here that you may find additional support in since you and your husband are her guardians; here's the link: https://www.dailystrength.org/group/parents-whose-children-have-been-sexually-abused . Hope to see you there if it's something you feel could be helpful. My apologies if that's not part of what she and you are going thru. Sending you healing thoughts and prayers...