There are some basic steps here:

1. Get the other projects time line and create an exception plan to the current plan that you have (Get the risk log and pad those in the time line from Project B)
2. Get the Project A's stakeholders(Internal and External) approval of the Exception plan, listing the impacts of the project - this should take a couple of meetings to get the Executive, Senior User and Senior supplier agreeing to the same thing.
3. Now you should be ready to put the project on hold. One thing that you should be doing is setting a recurring status check on the other project, to see if the Exception plan that you put in place will actually work in order to mitigate any risk and inform the Project A's stakeholders.

There are some basic steps here:

1. Get the other projects timeline and create an exception plan to the current plan that you have .Get the risk log and pad those in the time line from Project B.
2. Get the Project A's stakeholders  (internal and external) approval of the exception plan, listing the impacts of the project - this should take a couple of meetings to get the executive, senior user and senior supplier agreeing to the same thing.
3. Now you should be ready to put the project on hold. One thing that you should be doing is setting a recurring status check on the other project, to see if the exception plan that you put in place will actually work in order to mitigate any risk and inform Project A's stakeholders.