Keeping tabs on is a common phrase that means to monitor someone or something closely. Antonyms for keeping tabs on can include ignoring, neglecting, overlooking, or disregarding. These words imply a lack of attention or interest in the subject at hand. In contrast, antonyms that suggest a more hands-off approach could include trusting, respecting, or empowering. For example, instead of keeping tabs on your employees, you could empower them to make their own decisions and trust that they will meet their goals. Ultimately, the antonym chosen reflects your attitude towards the person or thing being monitored and can impact the relationship between parties involved.