Dear student,
Removal of one ovary still allows a woman to continue to menstruate and to have children, as long as the remaining ovary is not damaged. If only one ovary is removed, the other ovary will produce the normal level of estrogen and progesterone. Initially the hormonal level and the cycles might be imbalanced but the reproductive cycle will be normal after sometime of the removal of one ovary.
However, women have no compensatory mechanism for the loss of one ovary, and the number of primordial follicles is finite, leading to a shorter reproductive life span in these women.
Regards.