Answered by: Maulana Javed ibn Nazir Kachhalia
If an unmarried woman wants to work outside of home, is it obligatory for her to ask for her father’s permission? If her father is not alive, then does she have to take anybody’s permission?
In Islam, the principle is that the woman should try and stay at home as she is not entitled to earn, rather the male figures at home are liable and responsible for her expenses.
Islam teaches us that, an individual who is capable of supporting the family or members of the family we should do this according to our own abilities and capabilities.
Spending and aiding our immediate family is essential and its part of charity and good actions.
In regards to your question; if your father is not alive then the Mahrams in your family will be your guardians and permission will need to be taken from them.
A woman’s mahram is a person whom she is never permitted to marry because of their close blood relationship (such as her father, grandfather, great-grandfather, etc., and her son, grandson, great-grandson, etc., her paternal and maternal uncles, her brother, brother’s son and sister’s son), or because because of radaa’ah or breastfeeding (such as the brother and husband of the woman who breastfed her), or because they are related by marriage (such as the mother’s husband, the husband’s father, grandfather, etc., and the husband’s son, grandson, etc.).
These are the ones mentioned in Soorat al-Noor, where Allaah says (interpretation of the meaning):
“… and not to reveal their adornment except to their husbands, or their fathers, or their husband’s fathers, or their sons, or their husband’s sons, or their brothers or their brother’s sons, or their sister’s sons…” 
So from the above, we come to know that you can ask your brothers, paternal uncles, grandfathers, maternal uncles and so on.
Only Allah knows best.
Written by Maulana Javed ibn Nazir Kachhalia
Checked and approved by Mufti Mohammed Tosir Miah
Darul Ifta Birmingham
Surah Al-Noor 24:31