Tense remark made by a very conceited person! (9)
I believe the answer is:
imperfect
'tense' is the definition.
(the imperfect tense is a grammatical tense)
'remark made by a very conceited person' is the wordplay.
I cannot quite see how this works, but
'by' could be 'per' (I've seen this in another clue) and 'per' is present in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for imperfect that I've seen before include "Deficient" , "Describing continuous actions" , "Having faults" , "Flawed, defective" , "being immature" .)