Black Ops 3 has a new asset called scriptbundles which seems to be used to automate scripted tasks, mainly fx and animation playing. However, you can also play animations manually by following this page.
First you need to import your custom animation by following the page BO3 | Adding custom animations.
You need to precache your animation in your script using the following line:
Add your atr file and xanim to your map's zone csv located at root/usermaps/yourmap/zone_source/yourmap.zone by opening it with a Text Editor and adding the line:
To compile your xanim and save your changes, run Link compile from Launcher at least once.
To play your animation on a script model, you simply use the AnimScripted() function: