There is an image of one of our staff that pops up in search results that is in relation to an old business that we don't really want featured.
Is there an approach to remove or try to push an image (or page for that matter) down in the SERP's / image SERP's?
You can make a request to remove your own content from Google search results, including a specific image. See this for more: Google Webmaster Tools - Remove an image from Google search results.
If it's content from someone else's site and you want the image removed for legal reasons, you can send a legal removal request to Google. If you want it removed for personal reasons, you can use the tool here (see the last option): Issues with Google Search.
