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A physics package for a compact cold atomic clock is hereby presented. The uniqueness of this package is its small dimensions that enable, for the first time, implementation of a primary cold atomic clock in a standard package of 3U height (=133mm). These dimensions are made possible by using an in-vacuum Microwave (MW) Loop Gap Resonator (LGR) whose length and diameter can be reduced from those of a typical resonator. Following our presentation of the design, we analyze the homogeneity of the MW field amplitude and phase. We find that the expected clock instability due to non-uniformity of the MW field is $\sim1.5\cdot10^{-14}$/day. Adding other clock errors, we estimate the total uncertainty of a cold atomic clock of this design will be around $\sim2\cdot10^{-14}$/day which results in a time drift of a few nanoseconds/day. Such a clock can serve as a primary-grade frequency reference, and may replace the cesium beam atomic clock and the GPS-disciplined rubidium atomic clocks.