Bigquery replace value in a column based on previous year date condition

If version = "ACT" an DATE is not current year i.e 07-2020 to 06-2021 then replace ACT with ACTA

You want a case expression:

select (case when version = 'ACT' and
                  extract(year from date_add(date, interval 6 month)) = extract(year from date_add(current_date, interval 6 month))
             then 'ACTA'
             else version
        end)

The logic is to add six months and extract the year to get the fiscal year. Do the same for the current date. When these are the same, then the date column is in the current fiscal year.

Base on sample data in your question - I assume your data column is just INT64. Consider below then

select 
  if(version = 'ACT' and div(date + 93, 100) != extract(year from current_date), 'ACTA', Version) as Version,
  date
from data    

if applied to sample data in your question - output is