The filter function of dplyr is handy for this.
library(tibble)
#> Warning: package 'tibble' was built under R version 4.1.2
library(dplyr)
library(stringr)
DF <- tribble(
~order_number, ~Location, ~Date,
"1234-", "x", "1/29",
"4567-", "y", "1/29",
"4910-", "z", "1/29")
DF
#> # A tibble: 3 x 3
#> order_number Location Date
#> <chr> <chr> <chr>
#> 1 1234- x 1/29
#> 2 4567- y 1/29
#> 3 4910- z 1/29
DF <- DF |> filter(str_sub(string = order_number, start = 1,end = 1) != "1")
DF
#> # A tibble: 2 x 3
#> order_number Location Date
#> <chr> <chr> <chr>
#> 1 4567- y 1/29
#> 2 4910- z 1/29
Created on 2022-01-29 by the reprex package (v2.0.1)