Tom Hagan is supposedly dead by the time we see GF3 it doesnt go into detail how he died but the transcript from the scene in the vatican between Michael and Harrison talking about Toms son Andrew goes like this
MICHAEL (to Harrison)
His father was a great lawyer.
HARRISON
I know…
MICHAEL
Didn’t live to see him ordained. I did. You ever seen one of those?
So, thats all we get
FH