Does a divorcee or widow need to cover her hair?
Yes.
Why would she need to cover her hair if she’s divorced?
Covering hair is not just for married woman but also for any woman once married. For an in depth explanation of this halacha please see the Ohr Yitzchak: http://hebrewbooks.org/pdfpager.aspx?req=1525&st=&pgnum=386&hilite=