Mine (TR3A stock cover) came with an aftermarket oil breather that fits the stock cover. I guess I wrongly assumed that your aftermarket cover had the same style oil filler/breather but it sounds like yours is just a cap.
On the TR4A, it has a closed system with a PVC and a slotted oil cap and pin hole (for moisture?) like yours. It also has a breather tube on the side of the cover that attaches to the PVC and does not have a road draft tube.
But on an open system like the TR3, there is no breather tube on the valve cover since it "breathes" through the roaddraft tube and the breather/oil fill.
Whew, you probably already know all this.
SO, on your new alloy valve cover, you will need a way for it to breathe as well. (assume you already know this too).
It sounds like the cover you have is for a later model TR engine. Does it also have a tube in the side above the intake? If you purchased this cover specifically for a TR3, ask your vendor if they have a proper breather available.
Your options are to purchase a bolt on breather (Offy style) the bolts to the side of the allow cover but looks "different" IMO. Also you can get a K&N rear end breather - looks like a mini air filter and attach it to a
breather tube on the side (like the 4A).
You also may be able to get a breather from one of the speedshops like jegs, summitracing, speedwaymotors dot coms that fits the 2-1/4" filler hole.