Spending on certain programs that is required by existing law is referred to as

The answer is mandatory spending.
Mandatory spending as the name implies is spending that is mandatory for the government by some existing law which prescribes that the programs must be financed by the government.  According to the data form 2014, 60% of the federal budget was used for the mandatory spending. Before the Social Security Act of 1935 the budget spending was discretionary but after it the mandatory spending increased.