I am looking for an expression that means "right after finishing something, start something". For some reason, the words "fresh off the heels" keep springing up but I googled them and it's not an expression.
Or the idiom:
on the heels of
The oral examination came on the heels of the qualifying exam.
Fresh/hot off the press
This might be what you're thinking of/looking for.
How about "Immediately thereafter"?