Bumper possibly clipped by old lady (4)
I believe the answer is:
mega
'bumper' is the definition.
I don't know anything about this answer so I cannot tell whether this works.
'possibly clipped by old lady' is the wordplay.
I cannot really understand how this works, but
'possibly' could be 'eg' (for example) and 'eg' is found in the answer.
'old lady' could be 'ma' (both can informally mean mother) and 'ma' is located in the leftover letters.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for mega that I've seen before include "Great - denoting a million" , "Great American" , "Terrific" , "'Excellent, colloquially (4)'" , "Very large (prefix)" .)