Is there ellipsis in this sentence?

[sophiehhrr]

We got a mortgage from the cheapest lender. After that, we made an offer on the house.

I was thinking yes, instead of 'After that' it could be 'After [we got the mortgage], we made an offer on the house.'

Is this correct?

[Abstract Idea]

----- I am not an English teacher -----

We got a mortgage from the cheapest lender. After that, we made an offer on the house.

I was thinking yes, instead of 'After that' it could be 'After [we got the mortgage], we made an offer on the house.'

Is this correct?

Ellipsis again? Cool. It would help if we made a series of exercises with answers in order to practice it. Well, let's try this one.

I am not sure your suggestion is correct, because the pronoun 'that' is there.
If I understand well, the stuff should be omitted, not substituted by a pronoun.
Maybe:
We got a mortgage from the cheapest [house] lender.
After that, we made a [rent] offer on the house.

I am not sure I clearly understood the meaning of the sentence. were you trying to rent or buy a house?
What does exactly mean a 'mortgage' in this context?

[Rosamond00]

We studied a similar example in linguistics. If my memory does not fail me, this case is substitution not ellipsis, because you have the word "that" referring back to "we got..."

Ellipsis occurs when there is no substitution for the omitted part. For instance: "The Elder sister was beautiful, the younger [sister was] more energetic." The bracketed part was omitted without a substitution.
You can find more here.

[sophiehhrr]

oh right i see, so i can't change or remove any of the words or that would be considered as substitution?

[Abstract Idea]

oh right i see, so i can't change or remove any of the words or that would be considered as substitution?

If you substitute something by another stuff, rather than omit it, than it is substitution, not omission. I guess that is what Rosamond00 meant.

[Abstract Idea]

What about

We got a mortgage from the cheapest [mortgage] lender.