Chase up
Definition 1 of 2
Pro Tip 1/3Business Context
Often used at work to refer to resolving or reminding about overdue tasks. 
I need to chase up the marketing report that was due yesterday.
Pro Tip 2/3Task Reminder
Implies a nudge to prevent something from being overlooked or delayed further. 
Don't forget to chase up the team about the project deadline.
Pro Tip 3/3Proactive Approach
Shows taking initiative to deal with something that's been ignored. 
She decided to chase up the forgotten invoice before the accounts closed.