ah these are some interesting phrasal verbs. And of course as phrasal verbs they can have very strange and different meanings depending on what other words we're using in the phrase. "keep TO time"/"Keep Time" - these i would say would be more normally used in musical contexts. "keeping time" or "keeping to time" are a reference to the speed and rhythm of the music that you are playing. You will see many musicians tapping their feet on the ground in order to "keep time" with the rest of the musicians present. keeping "on" time could be very similar, but a regional difference in this idiomatic structure. I could see someone using "keep on time" similarly to "keep to time"/"keep time" in a musical context, but i wouldn't do that myself. Usually the "on time" part is actually going to be more about not being late to an appointment, work, meeting or class (whatever, something scheduled at a specific time, like some activity or something) It would help a lot if i could get more context here, where are you pulling this language from?

Could you maybe give us a full sentence where 'keep to time' is used? Without context I have to say the phrase seems strange to me (native British English speaker). 'Keep time' can mean a few different things depending on the context, but 'keep to time' seems unnatural...

I agree with the others. "Keep to time" is not a normal phrase - - Also, I'm a musician, and it's not musical terminology either.

We would usually say ‘keep to the schedule’ or ‘stay on time’. ‘Keep on time’ is ok but better if you are talking about music. ‘Keeping (the) time’ is fine but has a different meaning. (Keeping track of the time, for example in a sport or game)

Both are used for keeping the beat or main thing rhythm with music. ‘Keeping time’ is generally used more than ‘keep to time’ but the meaning is pretty much the same.