I agree with @Jim Reynolds that the best choice will depend on some more context than you're giving in the question, but I can think of two ways to specify it relatively clearly and concisely:
1) "the hour before the current hour" seems to describe it relatively cleanly and unambiguously, though it will depend on whether "the current hour" is an acceptable phrase to describe the "anchor time" of your period
2) "the previous whole hour" would likely work in many situations if you are speaking to a precise or literal audience (e.g. software engineers) who would recognize the phrasing as an attempt to describe a time period (a "whole hour" that presumably starts with minute zero and ends with minute 59) with a position relative to "now"
In essence, you're asking if there is an hour-based equivalent to the calendar month. Native speakers certainly would understand the difference between
She rented the car five times in the last month.
She rented the car five times in the previous calendar month.
There is no direct equivalent for hours in English (there is no common phrase such as the "clock hour" for instance), but I think in many cases using one of the two suggestions above would probably work.