Recreating a Destroyed Object with working click detector?

There's multiple alternatives.

such as, making the transparency of the exploded brick to 1, cloning and then moving them,

But in this case, you before exploding it; you can clone them somewhere, and then moving it back into the clickdetector. (depends on your script)

as you said, "Even though the model has one. So I can't blow up the new one."

Make sure the part has the same exact name as the one in the explosion script, also add a :WaitForChild() function

script.Parent.MouseClick:connect(function()
brick = script.Parent.Parent.Part -- assuming that the part is in a model

brick:Clone().Parent = game.ServerStorage -- or clone it anywhere you want,
-- explosion script here
wait(3) --after a few seconds
if game.ServerStorage:FindFirstChild("Part") then
game.ServerStorage.Part.Parent = script.Parent.Parent
if game.ServerStorage:FindFirstChild("Part") == nil then -- just some printing to check
print("part doesnt exist in serverstorage")
end
end
end)

Another alternative is to just create a new instance.

script.Parent.MouseClick:connect(function()

-- explosion script here

part = Instance.new("Part") -- start configuring all properties here
part.Anchored = true
part.Name = "Part"
part.BrickColor = BrickColor.new("Really red")
part.Parent = script.Parent.Parent
end
end)

Also make sure you clone it BEFORE you destroy it.

Thanks so @ast_raa much I'll work with this asap. A couple of follow up thoughts/questions.

You said:

"But in this case, you before exploding it; you can clone them somewhere, and then moving it back into the clickdetector. (depends on your script)"

I am cloning before destroying but I'm not rebuilding it until after the explosion. Also I'm not sure what you mean by "moving it back into the clickdetector" my click detector is in the model ... and thus in the clone.

Here's my code:

local backup = game.Workspace.TNT:clone() -- Make the backup    clone   
local newTNT = script.Parent  -- Define a new one


--[[ BEGIN : Blowing Stuff up ]]--

local TNTexplosion = Instance.new("Explosion")
TNTexplosion.Position = game.Workspace.TNT.band.Position
TNTexplosion.Parent = game.Workspace.TNT

for index, object in pairs(game.Workspace.TNT:GetChildren()) do         
    if object:IsA("BasePart") then 
        object:Destroy()  -- Destroy the parts within the model
    end                       
end

wait(0.2)

game.Workspace.TNT:Destroy() -- Destroy the model

--[[ END: Blowing Stuff up ]]-- 


--[[ BEGIN : See if they player is Dead ]]--

local deadCheck = player.Character.Humanoid.Health

    if deadCheck == 0 then
        msgis = player.Name .. " went BOOM!"
    else
        msgis = "Be Careful " .. player.Name .. "!"
    end

g2penvt:FireServer(player,msgis) -- Send the message to the player's screen

--[[ END  See if they player is Dead ]]--


--[[ BEGIN : Recreate the TNT ]]--

wait(3) -- Don't rebuild the TNT right away...

newTNT = backup:clone() 
newTNT.Parent = game.Workspace 
newTNT:makeJoints()     

--[[ END: Recreate the TNT ]]--

The re-created (clone) model that is created after the wait does appear to be named the same.

It HAS the click detector just as the origional ... my click listener function just doesn't seem to be able to "hear" the click event from the new one.

I'll look into the :WaitForChild() function. I'm not totally clear on what that will do or where to put it but I'll read up on it.