Almost certainly yes.
From the transcript of Face the Raven:
DOCTOR: It's called a Quantum Shade. It's kind of a spirit. Once it's bound to a victim ... you could flee across all of time and all of the universe, it would still find you.
A creature that can lock on to a signal and follow it across all of time and space? Who does that remind you of? That's right, the Time Lords. They have more advanced abilities in travel through time and space than any other civilisation we know of. It sounds as though the Quantum Shade may have some of the abilities of a TARDIS.
The fact that the Doctor has such familiarity with the idea of a Quantum Shade could also be seen as suspicious ... or maybe not, since he knows an awful lot about all sorts of creatures.
Finally, again from the transcript:
ASHILDR: I made a deal to protect the street. They take you, I take the key so you can't be traced. I do as they tell me, and the street is safe.
What did the Time Lords give her in exchange for her capture of the Doctor? It must have been something that enabled her "to protect the street". And what does she use to preserve the peace on the street, other than the Quantum Shade?
So it looks like yes, the Time Lords supplied Ashildr with the Quantum Shade.