Depends.
Most Earls have ancestors who were promoted in the peerage, so they also have the title of Viscount or (less often) Baron. The secondary title will then be lent to the eldest son as a...
Earldom is passed down from father to eldest son so even if a daughter is the eldest she won't get the title she will just stay Lady [forename, surname]. The only way a female can get hold of the...