Will you . . . . . . . . my dog while I am on tour?

look out
look up
look on
look after

The correct answer is D. look after.

The other options are not correct because:

  • A. look out means to be careful or to watch out for something.
  • B. look up means to search for information in a reference book or on the internet.
  • C. look on means to watch something happen without taking part.

To look after something means to take care of it. In this case, the speaker is asking the listener to take care of their dog while they are on tour.