Joining contrasting ideas with が
が has another job: connecting one statement to the next.

Learn
After a statement, が can mean “but.” この 車 は 高い です が、いい です means “This car is expensive, but it’s good.” Finish the first idea, add が, then give the contrast.
Look at what comes before it. In 猫 が います, が marks the subject. In 高い です が, it follows a statement and connects it to what follows. The same particle form has different grammatical jobs.
Connecting が can also introduce background or soften what follows, so it does not always imply a sharp contradiction. A speaker may trail off with 行きたい です が…—“I’d like to go, but…”—leaving the rest for the listener to infer.
Examples
この 車 は 高い です が、いい です。
This car is expensive, but it’s good.
日本語 は 難しい です が、面白い です。
Japanese is difficult, but interesting.
行きたい です が、時間 が ない です。
I want to go, but I don’t have time.