You have a Tumblr site, and you'd like to make one of your posts "sticky" so it remains at the top of the list. This isn't one of the built-in features on Tumblr, but many custom themes include this feature. Some themes call these "featured posts" instead of sticky posts, but they are the same.
How to Get and Install a Custom Theme
There are a couple of ways to apply a theme. The first is through a "Customize" link on your Tumblr home page. Click "Customize" in the right-hand menu. This takes you to an editing page where you can browse a limited number of popular Tumblr themes -- some of which support sticky posts -- or edit the HTML of your theme. Some themes require you to copy and paste the code that makes the theme work, and this is where you replace your existing theme's HTML.
Other custom-designed Tumblr themes make it super easy for you. Some companies that create themes provide an install link that does all the work for you. Single A, Purely and Sense are three free custom themes that include featured posts.
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Single A Theme
Single A by Storyware is a highly customizable free theme with lots of features. You can display tweets, run Google Analytics, display blogs you follow and posts you like on Tumblr, and -- of course -- create sticky posts, which are called featured posts in this particular theme. Storyware offers a premium version of this theme that offers even more features, including a header image option and Instagram integration.
What sets the Purely theme apart is its magazine-style design with featured image support in text posts. Purely is a light theme; it is designed to ensure quick loading times for your viewers. It comes with Font Awesome icons, which minimize imagery that can bog down your page loads.
Unlike the Stoneware themes, Purely does not have an easy-install link. This theme requires you to copy and paste its source code into your Tumblr's HTML section.
Sense is a clean-looking free theme that offers featured posts. It's easy to install; you use the install link on its home page that does the work for you. If you're looking for something simple, this one might be for you.