It is crucial that you look at what clocks actually do. Be it a mechanical clock, a quartz wristwatch, or an optical clock, they always feature some kind of regular cyclical motion which is "clocked up" and displayed in some accumulated form as the time. A clock doesn't actually measure time's flow/passing/progress. It isn't some kind of gas meter. It doesn't have time flowing through it. Instead the internal mechanism is a called a movement. It clocks up local motion, that's all. Re what Grumpy said:
"It is true that the Universe has no global time. It is also true that time exists for every frame and it's all Relative time as described by GR. Farsight tried the same dodge, saying that because coordinate speed changes that lightspeed through spacetime(c) changes, and it doesn't. Time is part of spacetime(as described by GR), it exists, but each frame travels through it at it's own Relative pace. There is no global (we call it absolute) time. But time exists nonetheless."
Forget this. The universe has a global time in its expansion and the CMBR redshift. Frames don't actually exist in any real sense, relative time is little more than relative local motion which is reduced by macroscopic motion through the universe. The speed of light through space varies, nothing moves through spacetime, it's static. You could say time is part of spacetime but the latter is an abstract thing, it isn't what space is. As for time existing, I think it's reasonable to say time exists like heat exists, but I think it's wrong to say it's fundamental like space is. Despite what Minkowski said, we live in a world of space and motion. Let me try to put it more succinctly: things move, sh*t happens, that's it.