Is it a site like wordpress or wix, or built from scratch?
If the latter, assuming they have the new image file, it would need to be uploaded via FTP to wherever their server stores images. Theoretically just replacing the image should be enough, but dimensions might be different so you would have to account for this.
If you simply want to put an image within the HTML document, it would go like so:
Code:
<img src="/images/newSRLlogo.png">
It honestly depends on the CSS/HTML structure of the website, how they chose to handle their images, et cetera.
For example, my background on my website is stored at srlclarity.com/images/banner.jpg
In my CSS directory, within style.css, I have the following code:
Code:
#header-wrapper
{
background: url('../images/banner.jpg') center center;
background-size: cover;
border-bottom: 4px solid black;
}