Hi,
Have you tried this plugin? Although I’ve not personally used this one, it seems like it might do the trick?
https://wordpress.org/plugins/mystickymenu/
If you feel comfortable digging into the code a bit, you could also try this tutorial to help get you started.
http://ozzyrodriguez.com/tutorials/fixed-header-wordpress/
Hope this helps get you started.
I tried the plugin but I cannot figure out the code to select so that only the menu stays sticky and not the whole header… any suggestions?
Thanks for your help!