Praise be to Allah the Lord of the Worlds.
A wife is allowed to observe voluntary prayer without husband`s permission. However, there is a difference between the ruling on wife`s observance of voluntary fast without husband`s permission and voluntary prayer since the time of fast is longer and the husband could be harmed as a result:{He is prevented from being intimate with her, because he would not want to spoil her fast.}. Therefore, seeking husband`s permission is limited to voluntary fast. The evidence for this is what Al-Bukhari narrated from Abu Hurayrah (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “It is not permissible for a woman to fast when her husband is present except with his permission.”
On the other hand, she is allowed to observe voluntary prayer without his permission because its time is short. It is stated in {Tohfat Al-Mohtaj}, a Shafie book, "Rather, it is not permissible for her to fast when her husband is present except with his permission, because he could be harmed as a result….However, she is allowed to observe voluntary prayer without his permission because its time is short." And Allah the Almighty knows best.