The 5e PHB states on page 63 about War Priest:
When you use the attack action, you can make one weapon attack as a bonus action.
So this rules out any beasts making a bonus attack after a multiattack, but what if an Awakened Tree for example uses his action to make a Slam Melee Weapon Attack. Can the player then make a second slam attack as a bonus attack?
I believe this would qualify and the beast's weapon attack would be considered as a valid triggering attack to create a bonus attack. The MM pp.10-11 says
The most common actions that a monster will take in combat are melee and ranged attacks. These can be spell attacks or weapon attacks where "weapon" might be a manufactured item or a natural weapon such as a claw or tail spike (emphasis mine)
What do you think? Can a Druid/ War Cleric Multiclass use the War Priest ability to make a bonus attack while wildshaped?
Best Answer
Yes, you can use War Priest but not if you use Multiattack
Taking a cue from András's answer, the attacks listed in a creature's stat block are not Actions but attack modes or melee attacks. Here's what I think you're missing:
Page 192 of the PHB defines the Attack Action:
The PHB further defines what a melee attack is and, in page 195, it explicitly states that:
With the above reading, the PHB confirms that Claw, Gore, Bite, and Slam are melee attack options that can be chosen when a creature uses the Attack Action and therefore able to trigger War Priest.
But this is where it gets weird:
Multiattack is a distinct Action that details what attack options are used by the creature when the creature uses Multiattack (not the Attack Action!). Since it is a separate Action (like Ink Cloud and Swallow) it cannot trigger War Priest.
This means creatures using Multiattack cannot trigger War Priest; they must use the regular Attack action and then use a Bonus Action to attack with War Priest, but this obviates the need to use War Priest as the Druid/Cleric can already attack twice with Multiattack.
As pointed out by KorvinStarmast, a beast with different attack options in the Multiattack Action like the Brown Bear could potentially get a slight damage increase if the Druid chooses not to use Multiattack (Claw [2d6+4] + Bite [1d8+4]) but instead use War Priest to attack twice with Claw (4d6+8). This allows for a unique dynamic that a Druid/Cleric can use during combat, when needed.