It goes to the expansion tank which I think is under the seat. Do not ride the bike with this disconnected.
Don't block it off !! it allows coolant to flow to the expansion tank when the engine gets hot and then draws it back as the engine cools. If you did block it off pressure would build up in the system and you could burst a hose or split the radiator. You must connect it to the expansion tank and make sure the tank is filled to the maximum mark with the motor cold.
If you're talking about the smaller hose that exits at right angles just by the thermostat (fat bit of the big hose)….. It doesn't allow anything to flow into the expansion tank. It should be connected to the spigot on the metal pipe that's attached to the water pump. Find your water pump, move towards the front wheel along the length of the metal pipe. It has a spigot pointing rearwards. That rubber pipe runs down between the carbs and the head and is secured to the spigot using a jubilee clip. Behind your carbs you'll see a clip that's there to hold the hose back against the head. It allows coolant to return without entering the radiator (before the thermostat opens) Please don't connect it to the expansion tank. The only connections to the expansion tank should be one small hose from the spigot just next to the radiator cap (which is visible in your photo) and another small hose which is the overflow and exits down by the swingarm spindle. Stu
Not wishing to labour the point but I'm keen for you not to trash your bike.... the big arrow is pointing to the other end of that hose.... you can't see the spigot because it's behind the fairing support bracket.
Haven't checked my facts but I tend to agree with Stuart. In fact you can just see the screw head for the relevant jubilee clip for the hose along the bottom extremity of the picture above just below the left bolt head for the fairing bracket, the projecting bolt below the right bolt head on the bracket is where the metal pipe fastens into the water pump. As it stands you will lose coolant from the outlet pipe by the radiator cap as soon as the engine gets hot. That should connect to the under seat reservoir. Have a look at www.worldoftriumph.com in the parts section to see if the schematic of the cooling system helps you. Had a look at the Sprint 900 section but it may (or may not - I didn't check!) be clearer in the Trident 900 section, or even the Daytona or Trophy sections.