How to add minutes to the time part of datetime

Use DATEADD:

SELECT DATEADD(mi, @increase,   @shift_start_time);

db<>fiddle demo

Using dateadd:

DATEADD(minute,@increase,@shift_start_time)

the first argument can be chosen among: year quarter month dayofyear day week weekday hour minute second millisecond microsecond nanosecond

please check https://learn.microsoft.com/en-us/sql/t-sql/functions/dateadd-transact-sql?redirectedfrom=MSDN&view=sql-server-ver16

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