If you hesitate, you do not speak or act for a short time, usually because you are uncertain, embarrassed, or worried about what you are going to say or do.

If you hesitate to do something, you delay doing it or are unwilling to do it, usually because you are not certain it would be right. If you do not hesitate to do something, you do it immediately.

You can use hesitate in expressions such as 'don't hesitate to call me' or 'don't hesitate to contact us' when you are telling someone that they should do something as soon as it needs to be done and should not worry about disturbing other people.