Dealing with change in a dependency

You could make your package work with both new and old versions.

your_existing_function <- function(..., cool_new_feature = FALSE) {
  if (isTRUE(cool_new_feature) && packageVersion("otherpkg") < "1.0.0") {
    message("otherpkg >= 1.0.0 is needed for cool_new_feature")
    cool_new_feature <- FALSE
  }
  # the rest of the function
}

your_new_function <- function(...) {
  if (packageVersion("otherpkg") < "1.0.0") {
    stop("otherpkg >= 1.0.0 needed for this function.")
  }
  # the rest of the function
}