I am replacing bathroom faucet with American Standardfaucet. My shut off valve has a tapered connection and will not accept the new faucet connection-threads will not reach. Is there an adapter or do I have to replace shut off valve
That's a flare fitting on your existing valve. You may be able to find an appropriate adapter, but I couldn't dig anything up very easily.
The valve looks to be attached to your supply line with a threaded connection, so it should be fairly simple to replace the whole valve using a new valve with a threaded connection. Shut off house water, unscrew this one, clean the threads and apply new thread sealing tape, screw on the new one.
If for some reason you cant/don't want to replace the valve you could make an adapter with a short piece of copper tube. Flare it ( need a flare tool.. ) use a flare nut, then use a compression union or a sweat copper to compression fitting on the other end.
Also if the old copper line is salvageable you could cut it and put a compression union on that.
I don't like cobbling together adapters like that, but on the other hand there is risk of damaging the pipe from the wall if that old valve is stubborn coming off.