Hi @SarvagnaPamidi-7119
The first solution that comes to mind is to add an 'If Condition' to your pipeline A or create a new pipeline and add Pipeline A and the condition activity to it (as shown in the example). The adjusted or new pipeline should have a trigger on it that is set to every day. The 'If Condition' activity checks if the current date is the first of the month. If so, it should activate your pipeline B.
Here is an example:
The code in the If Condition activity could be: @equals(dayOfMonth(utcnow()), 1)
Maybe there are better suited solutions, but I think it is not possible to succeed with only triggers. There should be a condition somewhere.
Hope this helps.