A PostgreSQL replica’s max_connections setting must be greater than or equal to the primary’s setting; if the value is increased on the primary before being changed on the replica it will result in the replica becoming inaccessible with the following error: 
FATAL:  hot standby is not possible because max_connections = 1000 is a
lower setting than on the master server (its value was 2000)
Our SRE Team is alerted when a replica fails for this reason and will take action to correct the situation (generally by increasing max_connections on the replica and notifying the user). To avoid this issue, you need to update max_connections on the replica Database to the higher value before updating the value on the primary.