You can reset the levels of the column you want to sort.
library(dplyr)
NUMBERS <- sample(1:11)
DF <- data.frame(Fac = paste("P", NUMBERS, sep = "_"), stringsAsFactors = TRUE)
DF
#> Fac
#> 1 P_6
#> 2 P_4
#> 3 P_5
#> 4 P_7
#> 5 P_8
#> 6 P_10
#> 7 P_3
#> 8 P_9
#> 9 P_11
#> 10 P_1
#> 11 P_2
arrange(DF, Fac)
#> Fac
#> 1 P_1
#> 2 P_10
#> 3 P_11
#> 4 P_2
#> 5 P_3
#> 6 P_4
#> 7 P_5
#> 8 P_6
#> 9 P_7
#> 10 P_8
#> 11 P_9
DF <- DF %>% mutate(Fac = factor(Fac, levels = paste("P", 1:11, sep = "_")))
arrange(DF, Fac)
#> Fac
#> 1 P_1
#> 2 P_2
#> 3 P_3
#> 4 P_4
#> 5 P_5
#> 6 P_6
#> 7 P_7
#> 8 P_8
#> 9 P_9
#> 10 P_10
#> 11 P_11
Created on 2022-04-16 by the reprex package (v0.2.1)