The New Nick Carter Library actually features Trimble, or Trim Carter as the detective. Trim is Chick Carter's son, and Chick Carter is Nick Carter's adopted son, so Trim is essentially Nick's grandson.
This particular story has Trim cleaning up a plot thread and tracking down the accomplice of a criminal he had already captured in a previous story. It has a lot of typical stuff for an adventure in the frozen north, eskimos, a kayak, sled-dogging, a polar bear, minus 50 degree weather and snowstorms, and floating on an ice floe. Of course, these may not have been too stereotypical back in 1897! The writing is fairly clean and easy-to-read, without a lot of purple prose or dry exposition.
Link to the book:
New Nick Carter Library 04 - Trim Among the Esquimaux