1. assume responsibility for dealing with something
leave it with me to sort out
Use expression 'leave it with me' when you want to assure or someone else that you will take responsibility for an action. If you say leave it with me it means you intend to deal with the matter at hand or address the problem. For example, if you are working in an office in a supervisory role and someone comes to you to complain about another employee you might say 'leave it with me' as a way of promising you will address the issue with the other person involved.