The most common and most likely answer to this crossword clue is the 4 letter word BIRR
B
I
R
R
Buddy explains!

The straight part
We know that "Vigorous activity, quite often American/money in Addis" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case vigorous activity, quite often american/money in addis = birr.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does BIRR mean?
BIRR noun- Force, vigor, energy
- A strong wind.
- The force of movement; rush, impetus, momentum, driving force
- A thrust or push.
- A whirring noise
- A strong trilling.
- To make a whirring noise; make a noise like that of revolving wheels, or of millstones at work.
- To lurch or set to spinning.
- The currency of Ethiopia, divided into 100 santims.