How to make my LocalScript wait for the Character and working more than once?

Okay guys hoping you can help me out here, I need this part

repeat wait() until player.Character ~= nil

in my LocalScript because it later complains about in Server log

-- character not being a valid member of Model

from this line

local character = player.Character

I understand why this is occurring, the script is running before the Character is created, that is why I have that repeat up there. The issue with the repeat is that, after the Character is no longer nil, the script will never re-run. So, if the player resets, the LocalScript is useless because of that statement because it won't run again. What else can I do?

Full Script

local player = script.Parent.Parent
repeat wait() until player.Character ~= nil
local character = player.Character
local humanoid = character.Humanoid
local repStorage = game:GetService("ReplicatedStorage")
local event = repStorage:WaitForChild("RemoteEvent") 

game.Players.LocalPlayer.Character.Humanoid.Health==0 do wait(); end
humanoid.Died:connect(function(Died)
    print('Checking if the boss dies')
    for i, v in pairs(game.Players:GetChildren()) do 
        if v.TeamColor == BrickColor.new('Bright red') and player.Name == v.Name then       
            event:FireServer()
        end
    end
end)