What does the Install Loyalist casus belli cost?

piety; the amount depends on the titles, claims and distance, worked out when you declare.

Casus belli · Struggles

Install Loyalist

The war is called “Install Loyalist in …”

Install Loyalist is a casus belli in Crusader Kings III (struggles). If the attacker wins: The Ruler of … is deposed and replaced with a Fp3 Struggle Supporter of the Caliph. If the defender wins: … remains under the impartial rule of the defender. Declaring it costs piety. The war goal is worth 75% war score. Patch 1.20.0.3, from game/common/casus_belli_types/05_fp3_wars.txt.

Quick answers (3)

What do you get for winning a Install Loyalist war in CK3?: The Ruler of … is deposed and replaced with a Fp3 Struggle Supporter of the Caliph (patch 1.20.0.3).
What happens on a white peace?: … remains under the impartial rule of the defender.
What does the Install Loyalist casus belli cost?: piety; the amount depends on the titles, claims and distance, worked out when you declare.

How the war ends

Attacker wins

The Ruler of … is deposed and replaced with a Fp3 Struggle Supporter of the Caliph.

White peace

… remains under the impartial rule of the defender.

Defender wins

… remains under the impartial rule of the defender.

If the war becomes invalid

The … has ended: it was no longer valid to continue.

Who can declare it

The game shows no text of its own for these conditions; the script is below.

Every struggles war (the group's allowed_for_character) (8 lines of game script)

can_use_struggle_cbs_trigger = yes
herders_and_tributary_constraints = yes
pam_personal_pacifism_offensive_war_ban_trigger = yes
tgp_dynastic_cycle_offensive_wars_ban_trigger = yes
tgp_war_ban_all_ministers_trigger = yes
NOT = {
	government_has_flag = government_is_theocracy
}

As written in game/common/casus_belli_groups/00_casus_belli_groups.txt.

Attacker (allowed_for_character) (12 lines of game script)

has_trait = fp3_struggle_supporter
exists = title:d_sunni.holder
OR = {
	is_ai = no
	opinion = {
		target = title:d_sunni.holder
		value >= 1
	}
}
NOT = {
	government_has_flag = government_is_landless_adventurer
}

As written in game/common/casus_belli_types/05_fp3_wars.txt.

Defender (allowed_against_character) (5 lines of game script)

is_landed = yes
this = top_liege
NOT = {
	has_trait = fp3_struggle_supporter
}

As written in game/common/casus_belli_types/05_fp3_wars.txt.

Cost to declare

Costs piety. The amount is worked out when you declare (by the titles targeted, claims, distance and more), so the script is shown as written:

Cost (18 lines of game script)

piety = {
	add = {
		value = major_piety_value
		desc = CB_BASE_COST
	}
	if = {
		limit = {
			scope:defender = {
				has_variable = last_explicit_defied_caliph
			}
		}
		multiply = {
			value = 0.5
			desc = cb_rejected_caliph_discount
		}
	}
	multiply = common_cb_piety_cost_multiplier
}

As written in game/common/casus_belli_types/05_fp3_wars.txt.

Source: game/common/casus_belli_types/05_fp3_wars.txt and the English localisation, Crusader Kings III 1.20.0.3. “The attacker”, “the defender” stand where the game names the character; “…” marks other words it fills in during play.