These THAT chip's have a log detector, from which is derived a DC voltage which controls the VCA. (Everything is matched to about 7mV/dB from memory.) That voltage is then run through some circuitry to set threshold and ratio, you end up with a control voltage which is applied to the VCA to give gain reduction. Looking at your circuit this looks like the voltage on R16.
If you want to indicate gain reduction on the meter, you need to drive the VU meter such that the meter is at 0 (which needs a standing current through the meter) when this voltage is zero, and then REDUCE that current as gain reduction is applied to the VCA. This is basically an exercise in applying scale, DC offset, and possibly inversion to get the results you want. It can all be done with standard inverting and non-inverting opamp circuits, perhaps with some preset adjustments.
The easiest approach would be to build this circuit and then measure the control voltage with various settings to determine the polarity and mV/dB of control voltage, and then figure out how to scale that for you chosen meter. A bit of fiddling with a calculator and maybe a little trial and error should get you there.
(NB you DON'T want to use the actual control voltage of the VCA, because that ALSO contains a component of "makeup gain" (from VR8) which is NOT part of "gain reduction" as metered on a classical compressor. You only want the "gain reduction signal, after applying threshold/ratio, which is on the common contact of SW3A.)