If I had to guess, your problem is either one of these things:
1. You didn't place a direct link to your gif inside that HTML tag. For example:
<img src="http://www.cloudservice.com/yourcloudaccount/giffolder/funnybanana.gif">
So, go to the pic or gif. Right click on it and then select the option Copy Image Link.
This is the safest way to make sure you're copying an image's direct link and not the just the link of the website/cloud service/etc...
2. Please, for the love of God, do not use Discord to host your images. I'm not sure if that's your case, but use a proper Cloud service like Imgbb, Imgur, MEGA, Dropbox, even Google Drive if you want and feel comfortable. There are many options out there that you can choose from.
I hope this helped. (ᵔ⩊ᵔ)