How can i make it so a group member will only be able to click it?

Use the Player:IsInGroup() function like so:

local groupId = 123 -- change to your group id
local gate = script.Parent.Parent.Gate

script.Parent.ClickDetector.MouseClick:Connect(function(plr)
	if plr:IsInGroup(groupId) then
		gate.Transparency = 1
		gate.CanCollide = false
	end
end)

If you want only specific ranks to be able to click it, use Player:GetRankInGroup() and do something like this:

local groupId = 123 -- change to your group id
local minRank = 100
local gate = script.Parent.Parent.Gate

script.Parent.ClickDetector.MouseClick:Connect(function(plr)
	if plr:GetRankInGroup(groupId) >= minRank then --if its equal or greater than
		gate.Transparency = 1
		gate.CanCollide = false
	end
end)