Does tube testers tell how much life is left for tubes?

You can take a brand new tube that tests perfectly (this is after all the way they leave the factory) put it in your amp and watch it blow the first week.

You can take another brand new tube that tests perfectly put it in the same amp and it lasts five years.

So yes you can use a tube tester to tell you how long a tube will last. Accurate to within 5 years.

The best measure of the condition of the tube is to measure transconductance.  Transconductance is a measure of the change in current flow across the tube ("plate current") for a given change in grid bias.  (I didn't look that up, so if I got it wrong, mea culpa.) Since it is a current divided by a voltage, its units are inverse to ohms, called "micromhos".  So far as I know, the only vintage tube testers that measure transconductance are Hickok brand and a few other brands that were actually made by Hickok for that brand.  So, you start with a table of transconductance readings for the particular tube under test, and you use the tester to find out whether that tube sample meets spec.  Typical Hickok testers have a big analog meter on the front panel and will indicate to the user whether the tube needs replacement if it is too far under the standard transconductance for that tube type.  Many times a perfectly good usable tube will measure a little below max transconductance.  When the tube is really at death's door, it will look to be very low in transconductance.  Another way to test a tube is simply to measure current and voltage while it is in the circuit where you are using it.  That's actually better than using some ancient uncalibrated tester.  The old testers almost never can test a tube under the actual conditions of its use in circuit, because they usually cannot develop adequate plate voltage or current for high current tubes to work best.

A calibrated TV-7 was good at that, checking life and shorted tubes, i have used one for some time, could not match tubes though. If going into tube testers and want matched tubes better invest on a modern one that can measure in actual conditions, or close, transconductance, plate current, leakage and mu.
Otherwise use your tubes close to the safe end of their lives.
Tubes are not created equally so you cannot tell from heater element glow if they are good or bad.
Actually you cannot tell if they even work.
You could monitor though a specific tube for changes in glow with usage.

Thanks for the info (even to MC).
I have two tube testers. One from Knight and one from Superior Instrument. Both is I guess made in late 50s or early 60s. They don’t have transconductance readings. They tell whether tubes are good or bad, but they don’t tell how much life is left.
If in doubt, I would just purchase new tubes to be safe.
The new (old) preamp I just bought (A.I. M3B) is recommended to have tubes replaced every two years. Yikes!

short answer is even the best tube testers measure the present degree of mutual transconductance of a test subject tube - it is a decent proxy for tube strength/freshness but it is a poor proxy for durability as a function of time

if you want to educate yourself more...

http://www.alltubetesters.com/articles/tester_guide.htm

http://www.jacmusic.com/Tube-testers/

https://shop.ehx.com/vacuum-tube-faq/ - see section on tube testing