tbh it looks gash, but the bare copper showing isn't really an issue as the back of the clamp assembly is all uninsulated anyway.
I'm guessing its two cables strapped together, which is why there are two (poorly crimped) crimps. you could do away with the crimps altogether and clamp the cables into the recess as it is designed.
Insulating tape is poo for this, it will end up a horrible sticky mess. You may struggle with heat shrink due to the differing size of the clamp and the cable. However, by the wonders of modern science, there is something called self amalgamating tape which would do the job. You stretch it then wrap it round, a bit like insulating tape, then it slowly all fuses together. Takes a bit of practice to look good (I'm **** at it) but thats the way to go, always use it when breaking into wiring looms or whatever.