How do i get my timer to work for my Combo System?

In your spawn() function, you don't have a loop to constantly check to see if it needs to reset their current combo. So it'll run a single time once you spawn the function, and of course since it's running only once as soon as you spawn the function, the passed time won't be passed your maxTime

With that being said, this should fix your problem

local uis = game:GetService("UserInputService")

local runservice = game:GetService("RunService");

local repstorage = game:GetService('ReplicatedStorage')
local events  = repstorage:FindFirstChild("Events")
local modules = repstorage:FindFirstChild("Modules")


local player = game.Players.LocalPlayer
    local char = player.Character or player.CharacterAdded:Wait()

repeat wait() until player:HasAppearanceLoaded()

local current  = 1
local cooldown = false

local startTime = tick()
local maxTime = 1.5

local animTable = {
        "rbxassetid://04540124455",
        "rbxassetid://04540153886",
        "rbxassetid://04540429673",
        "rbxassetid://4540628785" ,
        "rbxassetid://4540931147"  
}



uis.InputBegan:Connect(function(input)
    if input.UserInputType == Enum.UserInputType.MouseButton1 and not char:FindFirstChildOfClass("Tool") and not cooldown then
        cooldown = true

        startTime = tick()  --------TIMER SCRIPT[[
            spawn(function()
                repeat -- loop added so it's constantly checking
                    runservice.Heartbeat:Wait()
                until (tick() - startTime) > maxTime 
                startTime = tick()
                current = 1 
                print("waited too long, combo reseted to first animation")
            end)           ----------TIMER SCRIPT END]]


        local hum = char:FindFirstChild("Humanoid")

        local a1 = Instance.new("Animation")
        a1.AnimationId = animTable[current]

        local track  = hum:LoadAnimation(a1)
        track:Play()


            track.KeyframeReached:Connect(function(frame)
                if frame == "Hit" then
                    local part = Instance.new("Part")

                end
            end)
            track.Stopped:Connect(function()
                if current ~= #animTable then
                    current = current + 1

                else
                    current = 1 

                end

                print(current)
                cooldown = false
            end)
    end
end)