If I am guessing the context properly 'trace over' is probably the most appropriate description, rather than 'trace'.
I imagine this is from instructions similar to a join the dots exercise. Am I right?
If so, a better way to provide instructions would be to say:
Join the dotted lines to complete the monkey's tail.
However 'trace' is a verb commonly used to in children's drawing games. 'Tracing' is usually (in the context of children) creating a copy of an image by putting a semi-opaque piece of paper on top of an image, and then 'tracing over' the lines that can be seen through the top sheet.
However, in this context, the instructions are telling the reader to 'trace over' the dotted lines (literally draw a line on top of the existing dotted lines) to create a finished image. Because the instructions are to do something on top of something else, 'over' is the correct preposition to use.
It is not a phrasal verb. It is simply a verb followed by a preposition indicating where the tracing should be done in relation to the lines.
'Trace on' could also be used. In this context it means very much the same thing, but in other contexts something 'on' something would be touching the thing it was 'on', while something 'over' is often/usually a distance above and not touching.
For instance:
I am flying over the White Cliffs of Dover.
Means: I am flying in the sky above the White Cliffs.
I am flying on a magic carpet.
I am sitting on (touching) a magic carpet that is flying in the air.