The most common and most likely answer to this crossword clue is the 8 letter word CODPIECE
I've seen this crossword clue in The Times
C
O
D
P
I
E
C
E
More clues leading to the result CODPIECE
- Fake article providing cover under corporation, once
- Fish dish taken to church in an old man’s pouch
- Physician returns US weapon in pouch
- Article on fraud in personal cover
- Toolbox company, Germany, wants scrap
- Man put on sham cover for crown jewels
- Fake gun as fashion accessory once
- Payment method — coin pouch
- Pouch item from the chippy?
- Fishfinger perhaps, used to dress up meat and two veg
Buddy explains!

The straight part
We know that "cover under corporation, once" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cover under corporation, once = codpiece.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CODPIECE mean?
CODPIECE noun- A part of male dress in the 15th and 16th centuries, worn in front of the breeches to cover the male genitals.
- A conspicuous protection for the male genitals in a suit of plate armor.