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Catch up
has a few meanings, but they all involve getting closer to something or someone: like To reach someone or something that’s ahead. To get back on track after falling behind in tasks or activities.
Examples:
1- Serena Williams took a break from tennis, but she worked hard to catch up with the competition before returning to the court.
2- Scientists are racing to catch up with the rapid development of AI technology to address its challenges and risks.