You can use stringr() package, for example
library(stringr)
sample_year <- "1960 [YR1960]"
str_extract(sample_year,"^\\d{4}")
#> [1] "1960"
Created on 2019-12-08 by the reprex package (v0.3.0.9000)
If you need more specific help, please provide a proper REPRoducible EXample (reprex) illustrating your issue.