This is a jukugo word, which usually means on'yomi readings from the kanji, but in this case the second kanji can be read as either the on'yomi or kun'yomi. You haven't seen the kun'yomi for 家 yet, so here's a mnemonic to help you:
If you're renting a house, someone has to give you the keys and let you in and stuff. You're only renting, after all. So when they let you in they'll say, "Here's a shack for yah! (しゃくや) Enjoy!"
By the way, in the secondary reading, the しゃく goes to しゃっ. You'll see しゃくや more often, though.
You can't borrow money on a rented house.
"Tenants' Rights" simply means you have the right to rent a house, right?
I’m trying to talk to Salmon about renting a house instead of buying one, but she kind of keeps skirting the issue.