This is a rather simple task which you can probably find in other answers. Though, you can achieve what you want with data.table as follows:
library(data.table)
df = data.table( ID = 1:5,
x.2019 = seq(10, 50, by = 10),
x.2020 = seq(20, 60, by = 10)
)
# change column names conveniently
setnames(df, c("x.2019", "x.2020"), c("2019", "2020"))
# transform the dataset from wide to long format
out = melt(df, id.vars = "ID", variable.name = "time", value.name = "x", variable.factor = FALSE)
# cast time to integer
out[ , time := as.integer(time)]
# reorder by ID
setorder(out, ID)
out
#> ID time x
#> 1: 1 2019 10
#> 2: 1 2020 20
#> 3: 2 2019 20
#> 4: 2 2020 30
#> 5: 3 2019 30
#> 6: 3 2020 40
#> 7: 4 2019 40
#> 8: 4 2020 50
#> 9: 5 2019 50
#> 10: 5 2020 60
Created on 2022-01-20 by the reprex package (v2.0.1)