You could upload the image  into a picture library. You could then reference the image from the picture library in the Image Web Part. You could also create a hyperlink  to the image from the picture library.

I've already referenced the image  from the picture library in the Image Web Part. What I want from there is the ability to hyperlink  that image to another page, so when the image in the Image Web Part is clicked the user is taken to another page.

If I added that feature to the Image Upload web  part, would you find that helpful?

Why not use a CEWP and put your image  inside a </ href....> ; e.g.,
<a href="http://.........."><img src='/_layouts/images/ball_glass_reds.gif' alt='*' /></a>

Then export the resulting web  part. You can add  it to the web part  gallery so it can be used again.

I don’t think you can do that with the image  Web Part. However, the Content Editor Web Part will let you do what you want. First, insert the image using the CEWP Rich Text editor. Next, select the picture and then select Insert Hyperlink.

How do you get the CEWP? And how do you add  it to your web  parts
list? Sorry if this is a basic question. I'm fairly new to doing
anything with Sharepoint that is not pretty much out of the box.