It is obligatory for a Muslim woman to perform Ghusl after her menstrual cycle to be considered Tahirah.
Until she performs Ghusl, it is not permissible for her to have intercourse with her husband, as Allah Almighty says (interpretation of the meaning): "... and when they have purified themselves (from menses, have taken a bath) approach them (i.e. for intercourse) as Allah has ordained for you (i.e. in any manner so long as it is in the vagina)." [Al-Baqarah 2:222].
Purification does not simply mean the cessation of blood flow, but also the act of performing Ghusl afterwards. Once that Ghusl is performed and intercourse resumes, any Janabah that follows carries its own restrictions, including on reciting Qur'an, until the next Ghusl.