Leaking Shower

I have a 40ish year old shower with a diverter valve between the hot and cold stems. It is a central system (10 ce 3 bath stem).

I had a leaking bath tub. When i ran the shower, water would come out the bath tub spout and the hot water stem.

I replaced the valve stems for hot and cold. That resolved the water flow out of the valve stems. I replaced the valve stem with a central (11 ce 3 diverter stem). I have eliminated the flow of water out of the bath tub while shower is running, but noe there is a steady trickle out of the shower head while the bath is running.

Any ideas?

Welcome Elvin:
The diverter valve is probably covered with mineral buildup. If you can take that part out and clean it, you may get it to work again.
Glenn

Remove the diverter stem & seat, and replace them.

See this link starting at page 59 to match up your central diverter.
http://www.arpny.com/pdf/StemCatalog_A-F.pdf

If you know who the faucet manufacturer is/was, but can't find what you need in Redwood's catalogue, then...

Kissler is a major plumbing parts wholesaler in the US. They import a lot of plumbing parts that were formerly manufactured offshore before the faucet was discontinued or the company went belly up. They also manufacturer many of the brass plumbing parts themselves for discontinued and obsolete faucets. (For example, the American Brass Company went out of business in 1960, but Kissler still makes bronze seats for it's tub and shower faucets. Ditto for Crane two handle Dial-ese T&S faucets which haven't been produced for at least 10 years now.) Kissler has a $250 minimum order, so you won't be buying directly from them. You'll have to order the diverter through one of their retailers like Sexauer or Handyman Hank's. You live in New York, so you should be able to find one of their retailers locally. (I have to import some of the Kissler parts I need from the nearest retailer to me, which is in Minnesota.) Click on any of the online catalogues to download:

Kissler & Company Inc. - Downloads

I'm on dial-up with a 33K modem (which was considered "fast" at one time), and it takes me about an hour to download their 23 MB faucet stems catalogue. So, whenever I download another Kissler catalogue, I burn it onto a dedicated "Kissler" CD so I have it readily available.

I had a similar problem. But in my case, I think it was the crud buildup that was the cause. I realized that the bathtub shower was seldom used, hence I asked my wife to start using it more rather than the master bathroom shower. In time the leakage went away.