If I have understood correctly, OP is concerned that her DD has the potential to be comfortably at the top of her year group, but isn't.
As she is clearly clever enough to achieve this (at the moment, and fully accepting that things can change) one can only assume that there is something else holding her back - lack of confidence, self esteem, resilience or self motivation, a behaviour issue, a processing issue, a memory issue.
Really, it could be anything, but if the Ed Psych didn't identify anything specific then it is likely to be something that will come with maturity but a great start would be building her confidence to 'have a go', praising effort and yes encouraging social skills.
The only thing I would say is that there is a child in DS's class like this - his mother tells everyone how clever he is, and he is, but he consistently fails to meet her expectations because her expectations are too high, and he is clearly aware of it. I hope that he doesn't eventually stop trying because his best is never good enough. I am not saying that this is your situation btw, just pointing it out as a cautionary tale.