[BadVolt]

I have some movements with my question.

1st. Register an event to initialize hooking link clicks

EVENT_MANAGER:RegisterForEvent("IRememberYou", EVENT_PLAYER_ACTIVATED, HookChatLink)

2nd. Hooking itself.

local function HookChatLink()
    for i=1,#ZO_ChatWindow.container.windows do
        ZO_PreHookHandler(ZO_ChatWindow.container.windows[i].buffer,"OnLinkClicked",HookChatLinkClicked)
    end
end

3rd. Function to add item to the end of current list and resise ZO_Menu

local function HookChatLinkClicked(self, linkData, linkText, button, ctrl, alt, shift, command)
    -- thx Kentarii
    local linkType, _, _ = zo_strsplit(":", linkData)
 
    -- add our menu only to player linktype
 
    if linkType ~= CHARACTER_LINK_TYPE and linkType~=DISPLAY_NAME_LINK_TYPE then return end
 
    -- We want our item added after all items. So, wait untill they are created. Littly hacky, but... :banana:
    zo_callLater(
        function () 
 
            ZO_Menu:SetHeight(ZO_Menu:GetHeight()+22.3125)
 
            AddMenuItem("Rate", YourFunction)
 
        end
    , 1)
end

But now I have another problem... When I move mouse over new item it does not selects properly. It works sometimes, but I can't repeat it manually.