I was learning to develop animation for a Roblox game. That time I found this easy way of replacing the default animation with the new animations, which are created using the animation editor in Roblox Studio.
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The first step will be setting your rig. To animate your character, you have to have one rig that has the same bone structure as your character, so set up the rig. You can find my old post where I explained how to set up the rig for that. CLICKING HERE.
After setting up the rig, now play your game. When you play your game, select the explorer window and select your user name, rig. Copy the animated object.

After copying that, stop running the game. Now paste the animated object inside the StarterPlayer > StarterCharacterScript.

Now try to expand the animated object; you will find all the default animations.

Now let me change the run animation into the new animation that I want to play. For that, you first need to open the animation editor window. For that, go to the AVATAR window and select the animation editor. You don't need an image for that; it's too easy to identify.
After clicking that, you will find a new window opened in your game. Now select the rig that you added previously.
For more, CLICK HERE.