Why is my Leveling Script in my Game not working? (No Error Msg)

I think your problem is you are trying to modify player stats via local scripts. This will not work as the server is responsible for handling anything besides the character itself. You are also approaching it in a harder way. Based on your xp's required to level up you have a ~1.5 exponential growth to them. Instead of checking each level and each required exp for that level, just use some math to determine how much exp they would need to level up at their current level

-- In a script located anywhere
game.Players.PlayerAdded:Connect(function(player) -- Connect function to players joining
	local stats = player:WaitForChild("leaderstats") -- Wait for leaderstats
	local experience = stats:WaitForChild("XP") -- Wait for xp
	local level = stats:WaitForChild("Level") -- Wait for level
	experience:GetPropertyChangedSignal("Value"):Connect(function() -- Detect when experience value is changed, and when it is run below code
		if experience.Value >= 10 * (1.5 ^ level.Value * (1.5 ^ 1 - 1)) / (1.5 - 1) then -- Basically this checks to see if the players experience is equal or greater to the required exp for that level. I will bust the math down below
			experience.Value = experience.Value - 10 * (1.5 ^ 4 * (1.5 ^ 1 - 1)) / (1.5 - 1) -- If so, remove that much exp from the player (exactly that amount as not to remove exp over the required)
			level.Value = level.Value + 1 -- Level player up
		end
	end)
end)
-- This function will run any time the player gets exp, and if they have enough it will level them up.
--Now to explain the math
-- The formula you need looks like 10 * (1.5 ^ level.Value * (1.5 ^ 1 - 1)) / (1.5 - 1) 
-- It looks like this when you havent inputted your values.
-- b * (r ^ k * (r ^ 1 - 1)) / (r - 1)
-- b = the base experience required, in your case, 10
-- r = the exponential growth, in your case, 1.5
-- k = the current level
--With this in mind, you can change the values from b and r. Changing b will simply require more exp to start with, but each level up would be the same difference from having 1 or 1000. Changing r will make each level up require more or less experience than the last. So making that number lower will result in each level up only costing slighly more than the last, or making it bigger will make each level up cost way more. Using 1.5 is pretty close to your current formula.