A Muslim woman has to cover her hair while in sight of stranger men. They do not have to cover their heads near other women, or their brothers, uncles or father-in-law. They can be uncovered while reciting Quran.
The Glorified Allah commands:
“Tell the believing women to reduce some of their looks, and cover their private parts. Tell them not to uncover their beautiful parts except what is naturally seen. Tell them to put their headscarves onto their chests and not expose their beautiful parts except to their husbands, their fathers, their husbands’ fathers, their sons, their husbands’ sons, their brothers, their brothers’ sons, their sisters’ sons, their women, those in their possession, those male attendants that have no sexual desire to women, or children who are not yet aware of the private aspects of women. And tell them not to stamp their feet on the ground for their beautiful parts to be noticed. Believers! Return all together towards Allah, so that you may attain what you hope for.” (An-Noor/ The Light 24:31)
The Glorified Allah commands doing the following while reciting Quran:
“When you recite the Quran, seek refuge in Allah from the stoned satan.” (An-Nahl/ The Bee 16:98)
There is no other command.