I am a married woman with a very high sex drive whereby I am not fully satisfied with my husband even though we are sexually active. Is it permissible for me to do Mutah whilst being married?
Not at all. It is impossible for a married woman to even think about any sexual matter with any one apart from her husband.
Mut'ah is a type of marriage. As it is impossible for a married woman to marry another man while she is already married, it is impossible for her to do Mut'ah while is she is married.
You might need to consult a lady doctor for a medical advice to control your very high sex drive. It is always good to discuss such matters with your husband.
Wassalam.