The phrase "give the ax" means to dismiss, fire or terminate someone from their job or position. Its antonyms are phrases that denote the opposite of termination or ending, such as hire, recruit, appoint, retain, or promote. When someone is given the ax, they lose their job or position due to various reasons such as poor performance, misconduct, or downsizing. The antonyms for this phrase carry distinct positive connotations, as they relate to adding, maintaining, or improving people and organizations. So, while giving the ax may be a necessary but unpleasant action, the antonyms signify more favorable and optimistic outcomes.