Prompt acknowledgements of debt may be false (8)
I believe the answer is:
spurious
'be false' is the definition.
(I've seen this before)
'prompt acknowledgements of debt' is the wordplay.
'prompt' becomes 'spur' (I've seen this in another clue).
'acknowledgements of debt' becomes 'ious' (I am not sure about this - if you are sure you should believe this answer much more).
'spur'+'ious'='SPURIOUS'
'may' acts as a link.
Can you help me to learn more?
(Other definitions for spurious that I've seen before include "Plausible, but false" , "False, fake" , "Bogus" , "Not genuine or authentic" , "Forged" .)