It is not permissible for a male to take driving lessons from a female instructor or a female to take driving lessons from a male instructor.
Firstly, they are both in private, which is not allowed.
Secondly, the interaction is of a nature far beyond what Islam permits between two strangers.
Sitting in close proximity, great risk of ‘accidental’ physical contact, going to secluded/quite areas for practice.
Neither instructor or student can influence what the person wears in terms of clothes, perfume etc. Which only adds to the potential and actual temptations.
Also there is no need or necessity to take into consideration here, as women can learn from women and men from men.
Hope that helps.