Miss Snark's First Victim
Starting a sentence with the full name of the character being introduced sounds awkward. So does ending a call that hasn't begun in the text. It would flow better as, "After taking the call for the job, Sadie slumped back in her chair and..."
I like these first sentences a lot, and stating the full name doesn't bother me. I breezed right past it. But I would like a little more info about the call. I didn't know there was a phone call until it was over. I'd been picturing her standing somewhere looking down at the dead cat, not hearing about it over the phone. I have to reorient, and I need some help. It might be good if you could start the second sentence by letting us know that this is part of a phone conversation.But I like the MC's voice, and I would keep reading.
I still really like this, but there seems abrupt shift when we learn it was via the phone. I, too, picture the MC looking at the dead cat.
I like the voice! The phone part didn't bother me. "Client" alerted me that Sadie has a business (although we don't know what it is), so hanging up the phone seemed natural. You might consider adding a word like "frantic" to describe the call, to differentiate even more between calm Sadie and her client with a dead cat.
The cat got a lot of attention in the first two sentences. In the third, the cat left the scene. For me, that deflated the build-up. In order for me to relate to this character, I need the MC's reaction to express some sorrow or sympathy for the cat. Or the client. The emotion I'm getting is, "poor me."
Love the opening two sentences, but I was disoriented by the third. I wonder if Sadie couldn't express some sympathy to the caller instead, while you insert a description of her on the phone in the tag line? Then she hangs up and slumps back in the next line? It might take that disorientation away and would give us a sense of how Sadie interacts with a client.