There should never be a restart unless you perform one or the standby crashes. If you mean that you want to avoid a crash caused by a full disk on the standby, the answer is probably "no". Make sure that you have enough disk space and use monitoring.
Yours, Laurenz Albe
Is this because OP initially mentioned its RDS postgres, so in that case there is storage space restriction on 64TB(and 128TB in case of aurora postgres). So I believe this storage space combines data + WAL , so in that case as you mentioned, appropriate monitoring needs to be put in place.
Or else in the worst case scenario, if the storage consumption hit that hard limit , then there will be instance restart or crash?
