Check that you have a Troop with the correct Base Rarity to complete the Task.
Some Kingdom Power Tasks require you to collect Troops of a certain Rarity to complete them. If the task isn't completing and you've collected these Troops, check if they are the correct Base Rarity. Troops that are Ascended to another Rarity will not count for these Tasks.
Completing the Task
To check if you have Troops of the correct Base Rarity, Open the Troops menu > Select the Kingdom of the Task and Order by Base Rarity.
Troops with Stars around each dot at the top of the card indicate the Rarity of the Troop. For example, this Anointed One card is Base Rarity Epic but is Ascended to Mythic. As it's Base Rarity is Epic it will only apply to the Kingdom Power Task that requires Epic Cards.