If you see APU Essential that means the APU is running while in flight and a fault is detected which normally would have caused an automatic shutdown if it were not in essential mode. If you need the APU, keep it running. Otherwise, shut it down. Once it is shut down, it will not restart.
Everything here is from the references shown below, with a few comments in an alternate color.
Gulfstream GVII-G500 Airplane Flight Manual, Revision 4, August 29, 2019
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