How do I check for a game pass after the player respawns?

You can use player.CharacterAdded for give speed again

here is a example:

game.Players.PlayerAdded:Connect(function(player)
    print("Player added, player name is: " .. player.Name)
    player.CharacterAdded:Connect(function(char)
        print("Char of player " .. player.Name .. " added!")
    end)
end)

here is the script:

local gamepass_id = 0 -- Your gamepass id
local run_speed = 32 -- speed if player have gamepass

game.Players.PlayerAdded:Connect(function(player)
    player.CharacterAdded:Connect(function(char)
        if game:GetService("MarketplaceService"):UserOwnsGamePassAsync(player.UserId,gamepass_id) then -- detect if player have gamepass.
            char:WaitForChild("Humanoid").WalkSpeed = run_speed -- change the speed
        end
    end)
end)

Wiki pages:

MarketplaceService

UserOwnsGamePassAsync

PlayerAdded

CharacterAdded

Hope it helped :)

Errors? tell-me on comments.