as martin.R said, it'd be easier to do if you provided data for a reprex, but here's a simplified version. Replace the variable a# with your variable names and make sure that i is in first year:(most_recent_year -1)
This is base R, and not necessarily pretty, but it gets the job done:
df1 <- data.frame(a1 = rep(1, 9),
a2 = rep(3, 9),
a3 = rep(13, 9),
a4 = rep(54, 9),
a5 = rep(85, 9),
a6 = rep(16, 9),
a7 = rep(77, 9),
a8 = rep(88, 9),
a9 = rep(9, 9))
for(i in 1:8){
df1[[paste0("a",i+1,"_diff")]] <- df1[[paste0("a", i+1)]] - df1[[paste0("a", i)]]
}