(Did you catch the typo?)
Add a comma after running.
“What time is it?”
“Time for you to start running, apparently.”
If apparently was at the beginning of the sentence, you wouldn’t need a comma to separate it from the rest: “Apparently time for you to start running.” With it in any other position, however, you do need a comma, as in, “Time, apparently, for you to start running.” (Or, “Time for you, apparently, to start running.” Did you think only was unique in its ability to change the meaning of a sentence by changing its position?)