1. do the thing(s) that someone else is unwilling or unable to do, gather up or work on whatever is left undone or unused
I need you to pick up the slack
You might hear someone talking about taking up the slack at the end of a rope or line, but this is in terms of gathering what is left unused. If you pick up the slack from someone's work, it means that you are doing the things they were unable to do, either due to their lack of abilities or their time constraints. This expression is mainly about tasks, so in this context, it is less likely to be used in social situations (unless you're talking about tasks or complaining about work!).