"A woman in a convent" itself would give no palindrome, but "Nun" would give a palindrome as it is the same spelled forwards and backwards.
"Nun."
nun
NAN
nun
Nun
nun
nun
No, a convent is for women, a monastery is for men.
nun
Eve
The women could further their education.
Madam
madam
NUN
Convent, Cloister, or Nunnery