  We successfully demonstrate low-frequency noise suppression in the resonant
frequency fluctuations of a cavity-embedded Cooper pair transistor (cCPT)
driven at single-photon occupancy. In particular, we report a reduction in the
resonant frequency fluctuations caused by the internal charge noise over a
bandwidth of $\sim$1.4 kHz when the cavity is driven at an average photon
number $n=10$, and a bandwidth of 11 Hz for average $n=1$. The gate-dependent
tunability of the cCPT allows us to implement a feedback-scheme, derived from
the Pound-Drever-Hall locking technique. This reduces fluctuations due to
intrinsic charge-noise, which otherwise interferes with the cCPT's operation as
a near quantum-limited electrometer. We believe our technique can be
generalized to achieve frequency stabilization in tunable microwave resonators
that play a vital role in today's quantum computing architecture, thereby
moderating the limitations in detection caused by the intrinsic $1/f$-noise on
such circuit devices. The work discusses the various aspects relating to the
operation of a fully functional feedback loop down to the single-photon level.
