He was invited we hear and gave an estimate (7)
I believe the answer is:
guessed
'he was invited we hear and gave an estimate' is the definition.
The definition suggests a singular noun but the answer is not.
'he was invited we hear and gave an estimate' is the wordplay.
I cannot quite see how this works, but
'he' could be 'ed' (short for Edward) and 'ed' is found within the answer.
'estimate' could be 'guess' (guess is a kind of estimate) and 'guess' is present in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for guessed that I've seen before include "Made estimate or hazarded opinion" , "Hazarded, estimated" , "Conjectured" , "Reckoned, judged" , "took a shot" .)