A married Jewish woman is required to cover her hair.
If a woman that is married is going through the conversion process does she have to cover her hair?
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She should cover her hair the same way she keeps kosher -- she's not obligated as of right now, but she needs to get used to the lifestyle to make sure she's prepared for it. (It will also give her time to get used to the very different habit/sensation, for when she is obligated.)
(As to exactly what sort of hair covering is required -- or if there are leniencies about that -- that's a different question.)