Bagging promotion, that was impressive self-confidence (7)
I believe the answer is:
bravado
'impressive self-confidence' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how one could define the other.
'bagging promotion that' is the wordplay.
'bagging' is an insertion indicator (bag can mean to take or obtain).
'promotion' becomes 'ad' (short for advert).
'that' becomes 'bravo' (I can't explain this - if you can you should give a lot more credence to this answer).
'ad' inserted into 'bravo' is 'BRAVADO'.
'was' acts as a link.
Can you help me to learn more?
(Other definitions for bravado that I've seen before include "Showy boldness" , "Display of confidence or daring, often boastful and insincere" , "Swaggering confidence" , "Boastful threatening" , "Swaggering show of false courage" .)