To receive relevant and useful help, mention OS name, exact LOversion and save format (DOCX vs. ODF, extensions .doc(x) vs. .odt).
Your screenshot was taken without enabling View>Formatting Marks so I have no idea haw your header is structured. It is even not obvious whether it is an image or built as full text with a table.
There are several settings controlling the gap between header and text area but aesthetics is reluctant to suppress it completely. So, give a precise specification of what you want and attach a sample document corresponding to the screenshot. The screenshot shows a form of ribbon interface which suggests you’re practising direct formatting and are not familiar with styles. For all sophisticated or advanced layout/formatting, working with styles is mandatory for comfort, ease and peace of mind.
