to ask someone to do something that they promised to do but that have not yet done

If you don't hear from the builders this week, make sure you chase them up. 要是你这个星期还没有从施工人员那里得到消息，一定要催催他们。

I must chase my flatmate up about those bills and see if she paid them. 我得找我的室友问问那些账单的事，看看她是否付过账了。