紧 'tightly' +
追 'chase' +
不舍 'unwilling to let go', the four characters reinforce one image: a pursuer who will not slacken. Use it for physical chases (police, predators), competitive contexts (a rival closing the gap in a race or in market share), and metaphorical pressing (journalists, debtors, persistent suitors). Sometimes written
紧追不放.
