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?
Thank You so much Laurenz and Yudhi.
Yes its RDS and as you mentioned there does exist a space limitation of ~64TB but as Laurenz mentioned the only time the second standby may crash would be probably because of the storage space saturation and thus we need to have appropriate monitoring in place to find this and get alerted beforehand. And also a monitoring to see how much WAL gets generated per hour/day to get an idea of the usage. I am not sure how to do it , but will check on this.