It is a quite common need to compute service times based on how long time some machinery has been running. For example keeping track of number of motor starts, and total numbers of running hours. Or how many hours a projector lamp has been lit.

The OP do write:
"This design may be called as non-volatile timer." which signals a timer that isin't reset/cleared on power loss.

And the OP do write:
"But the timer must stop if this hour meter is unpowered. So, it actives only if powered."
which indicates that the clock should only run when power is applied.

The slow timer period of 1000 hours - 40 days - with power on until the buzzer activates also gives an indication that the OP may be interested in a service timer.

I may of course be wrong, since the original post could have been a bit more explicit. But if I'm wrong, then I'm not only wrong, but 100% lost to what the OP intended with the expression "non-volatile timer".

Since I can't be 100% sure that the OP wants such a function, I can only assume. So I did qualify my comment with the note about what assumption it was based on. If the assumption is wrong, then my post can obviously be ignored, but should inform the OP that a more explicit problem description is needed. Since assumptions are always dangerous, I always try to document any assumptions I make.

And since my post was based on an assumption - not 100% knowledge - I requested more information about the buzzer. A service timer would normally not trig an alarm cyclicaly every 1000 hours, but would trig an alarm and continue to run, until some form of reset function is activated after the equipment has been serviced or replaced.