Learn German: Obwohl das Haus alt ist, ist die Miete hoch. - Although the house is old, the rent is high.

The first ist is at the end of the first clause because obwohl pushes it there. The entire first clause (Obwohl das Haus alt ist) counts as the first block of information in the overall sentence. In German, the main verb must come in the second position, so the second clause has to start immediately with its verb, which happens to also be ist.

Does "obwohl" always push the verb to the end of the clause?

Yes. Obwohl (although) is a subordinating conjunction, just like weil (because) or dass (that). Whenever you use it, the conjugated verb of that clause must move to the very end before the comma or period.

Can I swap the two halves of this sentence around?

Absolutely! You can start with the main clause: Die Miete ist hoch, obwohl das Haus alt ist. Notice that in the main clause, the verb ist is in its normal second position. The obwohl clause still keeps its own verb at the very end.

Why is it just "hoch" and not "hoche" to match the feminine noun "die Miete"?

Adjectives in German only take endings when they come directly before a noun, like in die hohe Miete (the high rent). Because hoch comes after the verb here to describe the rent, it is in its basic, unchanged dictionary form.