They monitor an American game (8)
I believe the answer is:
checkers
'an american game' is the definition.
(I've seen this before)
'they monitor' is the wordplay.
I cannot quite understand how this works, but
'monitor' could be 'check' (synonyms) and 'check' is found within the answer.
The remaining letters 'ers' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for checkers that I've seen before include "They scrutinise" , "those on board" , "Draughts in America" , "American game" , "Quality assurance personnel" .)