Yes, in order to use animation templates created in After Effects, you must have a trial or licensed version of After Effects installed on your computer. If you have a Creative Cloud subscription, you already have an After Effects licence.
If you have a single product licence for Premiere Pro, you do not need a paid licence of After Effects. Instead, you can install the After Effects trial subscription. After the trial period expires, animation templates created in After Effects can continue to be used as long as the expired trial subscription remains installed on your computer. You can find more information here.