Is it permissible for a woman who sometimes uncovers her hair to wear a police cap that does not cover the head's hair, knowing that non-compliance with her superiors' orders may lead to her losing her job?

It is permissible for a woman to work as a police officer on the condition that her work environment is exclusively female, with no mixing with men, and that it does not require her to expose any part of her awrah (private parts), and that her clothes do not reveal the shape of her awrah. The default is for a woman to remain in her home unless there is a need. Similarly, it is not permissible for her to expose any of her hair in front of non-mahram men. She should seek permissible work where she can be safe from committing forbidden acts, for whoever fears Allah, He will make a way out for him and provide for him from where he does not expect. What is with Allah can only be attained through obedience to Him, and it is not permissible to hasten a destined provision by committing unlawful acts.