In DnD 5e a 1st level a War Domain cleric gets "bolts of inspiration" that allow an extra attack as a bonus action. This ability can only be used a limited number of times per long rest.
At 5th level a Blade Pact warlock can get the Thirsting Blade Eldritch invocation which allows the warlock to attack twice with their pact weapon.
If a character had all the prerequisites could they attack 3 times in one round? Twice with the attack action and once as a bonus action.
I know that extra attacks from multiclass do not stack. Is this an exception to the rule? Given the limited nature of the War Priest ability I don't think it would be terribly unbalanced but a character could occasionally elevate their burst damage.