The Gaggia TS steam and water taps can leak after prolonged use or storage.
The good news is that they are easy to rebuilt using only a couple of adjustable spanners.
First pull the control knob straight off. It is only held in place by friction fit onto the 7mm square shaft of the tap.
From the front of the machine, undo the chrome plated nut completely.
Inside the machine, undo the water pipe from the back of the tap. The tap can now be removed from the machine (there is no need to disconnect the water pipe or steam wand as these can pass through the body of the coffee machine).
The tap can now be separated into two pieces. The body of the valve will contain a chrome plated shaft, with two small o-rings (528765 in the diagram). The shaft can be carefully cleaned to remove any scale, and lubricated with food grade silicone grease before reassembly.
The main water/steam seal is (15mm OD, 6mm ID, 6mm thick) is part 528695. This should be possible to access by holding its brass holder by hand, and unscrewing its fixing with a spanner. This is clear if you have the parts in front of you.
As they say in all the best car manuals, reassembly is the reverse of removal.
If the above is too tricky, replacement taps are available on Ebay for about 30 GBP.