How to use the expression 一個上年
Most likely, 年 here was a typo of 午 in your book. 

一個上午 (a morning) make sense; 一個上年(a last year ) doesn't make sense.


'A year' can be any unspecific year
'Last year' is a specific year in the context of the speech. 
The phrase '一個上年' (a last year) contradicts itself.


Another explanation for '一個上年' to exist could be: '上年' here doesn't mean 'last year', but 'good year'( 上 as in 上等 - high quality). That is also unlikely, because '一個好年'is much more common way to describe a 'good year' 

If 一個上年 was not a typo, then it can only mean '上年'(last year) was a special year that was marked as a particular reference. 

For example: "再来一個上年, 公司就要破產 "-- "one more (year like) last year, the company will bankrupt"