[faithfulfrank]

The T & P valve is not working properly, and should be replaced. Rarely, after many years the spring can weaken, or the inside gets a bit of junk in it, and can drip.
You can CAREFULLY open it a bit and try to flush it out, but you risk the following;
1) Scalding water can come out of that pipe, burning you.
2) The dripping can increase to a constant flow or worse, thus needing a immediate replacement.

I recommend replacing the T&P valve. Any plumbing supply store or orange/Blue BigBox place has them.

You do not say of your tank is gas or electric.

If Electric, you can turn off the breaker, let the water cool off, then drain the tank to below the T& P valve. Then screw off the extension pipe, then screw off the t&P valve. There should be a tag on it with the rated Temperature and Pressure. You should replace it with the same. Install new one and reinstall the extension pipe. Turn the water back on, making SURE the tank is fully filled with water coming out of faucets, etc. Only then do you turn the breaker back on. Check the new valve for leaks.

If gas, the instructions are a bit different, depending if you have a powervent, or regular gas HWT.

If you do not feel comfortable doing this, call a plumber. If the tank is over 12 years old, and you need to call a plumber, you may want to just replace the tank, as it may be nearing the end of it's useful life. If you are going to pay a service call anyway.......

Note that the above condition can also be sometimes caused by water hammer, and that the T&P valve MAY be working properly. For water hammer, there are other solutions.

Frank