Definite evidence of a professor having nothing to hide (5)
I believe the answer is:
proof
'a professor having nothing to hide' is the definition.
I can't judge whether this defines the answer.
'definite evidence of' is the wordplay.
'definite evidence' becomes 'pro' (pro is a kind of evidence. I am not sure about the 'definite' bit.).
'pro'+'of'='PROOF'
Can you help me to learn more?
(Other definitions for proof that I've seen before include "Factual evidence" , "mathematical work" , "Positive evidence" , "Author may have to check this" , "Conclusive evidence or verification" .)