Idioms and Phrases with give notice
Inform or warn someone of something, as in He's prompt about giving us notice of any discrepancy in the accounts. [Late 1500s]
Tell one's employer one is quitting, as in Our housekeeper gave notice last week. This usage, first recorded in 1765, originally alluded to any kind of termination, such as a housing lease, but today is most often used for leaving employment.