Executing a SQL Job only once a month and after completion of a specific job
For SQL Server, you can specify On success action to go to the next step, only when the job step #1 is completed. There, use a date/time condition to execute the job#2

if (day(getdate()) = 1 and DATEPART(hh, GETDATE())= 1)
EXEC dbo.sp_start_job N'job#2'