After a Jaeger goes down and is destroyed by a Kaiju, what happens afterwards? What’s standard protocol for a situation like this?

Presumably whatever happened before the Jaegers were in service; throw everything that can shoot or bomb at it, including nukes, until it goes down.

We don't really know as the situation doesn't come up in the movies - the Jaeger are always able to prevail or call in reinforcements when they take casualties.

However, we are told that Kaiju can be brought down by 'conventional' means as humanity was killing them before the Jaeger program:

By the time tanks, jets and missiles took it down, six days and 35 miles later, three cities were destroyed. Tens of thousands of lives were lost. We mourned our dead, memorialized the attack, and moved on.

Presumably use of these methods would be the fall back option if no Jaeger were available or they were all defeated. It would be more difficult than taking down the first Kaiju and likely cause more human deaths and destruction as the attackers got tougher over time.

The Netflix anime is out soon and a third movie is not out of the question so this may be answered conclusively in the future.