The most common and most likely answer to this crossword clue is the 5 letter word STARK
I've seen this crossword clue in Financial Times
S
T
A
R
K
More clues leading to the result STARK
- Time in Channel island is bleak
- Complete legend, king
- Holy person going to biblical vessel’s stern
- Cold island imports temperature
- * mark ultimately grim
- Bald, completely naked Queen’s marched out
- It’s clear introduction of traffic is choking Channel Island
- Naked celebrity, the centre of jokes
- Principal knight is harsh
Buddy explains!

The straight part
We know that "Complete" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case complete = stark.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 STARK mean?
STARK adjective- Hard, firm; obdurate.
- Severe; violent; fierce (now usually in describing the weather).
- Strong; vigorous; powerful.
- Stiff, rigid.
- Plain in appearance; barren, desolate.
- Complete, absolute, full.
- Starkly; entirely, absolutely
- To stiffen.