Dear Sonali,
In the given situation two things emerge;
-the employee suffers from insecurity, or
-she harbours some grievances against the organisation,
In both the situation there is an urgent need to have an access to her psyche. This requires a thorough observation of her work and conduct as also views/observation of her peers/subordinates, if any/ superiors.Next step has to be your one to one discussion, not counselling, as you are firstly trying to diagnose the problem. The discussion has to be a repeated process, and on the basis of the derivations you have to take recourse to counselling, while doing so please also try to find out her confidante and use the latter in the process. After some time let her HOD appreciate her work and in due course inform about the recommendations for her promotion and also promote her with one more hand joining her team. Sure during this process the ice will be broken.
I agree this seems to be a long drawn process but you will agree that handling/ improving the psyche of a person consumes time.
Regards
S.K.Johri