Deficit admitted by company, American giant (8)
I believe the answer is:
colossus
'giant' is the definition.
('colossus' can be a synonym of 'giant')
'deficit admitted by company american' is the wordplay.
'deficit' becomes 'loss' (I've seen this before).
'admitted by' is an insertion indicator.
'company' becomes 'co' (abbreviation).
'american' becomes 'us'.
'co'+'us'='cous'
'loss' inserted inside 'cous' is 'COLOSSUS'.
(Other definitions for colossus that I've seen before include "Big statue" , "The - - of 19" , "Enormous statue" , "huge figure" , "Enormous figure" .)