We demonstrate a Ramsey-type microwave clock interrogating the 6.835 GHz ground-state transition in cold \(^{87}\) Rb atoms loaded from a grating magneto-optical trap (GMOT) enclosed in an additively manufactured loop-gap resonator microwave cavity. A short-term stability of \(1.5 \times 10^{-11} \tau ^{-1/2}\) is demonstrated, in reasonable agreement with predictions from the signal-to-noise ratio of the measured Ramsey fringes. The cavity-grating package has a volume of \(\approx \) 67 cm \(^{3}\) , ensuring an inherently compact system while the use of a GMOT drastically simplifies the optical requirements for laser cooled atoms. This work is another step towards the realisation of highly compact portable cold-atom frequency standards.