You are right that this use of there is related to there is, there was and similar constructions.

This construction (There + verb + subject) can be used with verbs other than to be—not only with modals combined with to be (There will have to be an investigation), but also (though less commonly) with other verbs, usually where the meaning is one of existence or appearance:

There exist only three examples.

 

After a while, there appeared a ghost.

 

Past the window there ran a llama.

You are right that this use of there is related to there is, there was and similar constructions.

This construction (There + verb + subject) can be used with verbs other than to be—not only with modals combined with to be (There will have to be an investigation), but also (though less commonly) with other verbs, usually where the meaning is one of existence or appearance:

There exist only three examples.

After a while, there appeared a ghost.

Past the window there ran a llama.