I know that it is a sin to not keep your gaze down when when one is looking at someone when that person is uncovered but is it still a sin if the person he/she is covering their awrah? For example if a man were to stare at a muslim woman, with lust, but that woman is covering everything except her face feet and hands, would it still be haram?
Yes, looking at the face, hands and feet of a non-mahram woman is forbidden when it will be accompanied by feelings of desire. That is agreed upon. According to some madhabs it is forbidden to look at them even when it is not accompanied by desire.
فطفق الفضل ينظر إليها، وأعجبه حسنها، فالتفت النبي صلى الله عليه وسلم والفضل ينظر إليها، فأخلف بيده فأخذ بذقن الفضل، فعدل وجهه عن النظر إليها
Al-Fadl started looking at her as her beauty attracted him. The Prophet (ﷺ) looked behind while Al-Fadl was looking at her; so the Prophet (ﷺ) held out his hand backwards and caught the chin of Al-Fadl and turned his face in order that he should not gaze at her
An exception would be when there is some valid reason, such as when looking at a potential spouse for purpose of sending the proposal of marriage.