The Z80A, rated for a maximum clock speed of 4 MHz, was a very widely used CPU in the 8-bit era.
The Z80H, introduced in 1986, was rated for a maximum clock speed of 8 MHz. This would at first glance appear to provide an excellent drop-in upgrade in cases where a computer is trying to be backward compatible with an older model, but now has fast enough memory chips to support the higher speed; you would get exactly double speed, which can easily be halved again for old hardware or software that depends on exact timing.
However, InfoWorld Oct 18, 1982, says, "Performance gained from the Z80H is expected to exceed that of the standard 4-MHz Z80 by four to six times. The new version of the Z80 has been designed to take advantage of 16-bit peripherals originally intended for Zilog's contender in the 16-bit race, the Z8000."
That seems to imply that it also decreases the number of clock cycles needed to carry out typical instructions. Is that the case? If it is, that would be good news for the extra performance, but bad news if you also need the ability to run at exactly the old timing; no way to have both abilities in the same chip?