The phrase "Leadership will hug you if you are eligible without a notice" is a metaphorical way of saying that good leadership recognizes and rewards deserving individuals, often unexpectedly.
In this context, "hug" symbolizes recognition or reward from leadership. Being "eligible" refers to having the necessary qualifications or fulfilling the required conditions, which could be anything from achieving certain goals, demonstrating particular skills, or embodying specific values.
The phrase "without a notice" suggests that this recognition or reward can come unexpectedly, reinforcing the idea that good leadership is always observant and appreciative of their team's efforts and achievements.