The most common and most likely answer to this crossword clue is the 6 letter word IMMUNE
I've seen this crossword clue in The Guardian
I
M
M
U
N
E
More clues leading to the result IMMUNE
- Setter’s married a foreign female — so complaint impossible?
- Leader of thieves is out of time holding up miners, resisting attacks
- Resistant setter’s married a Parisienne!
- Timmy discovered June won’t start, not being impressionable
- Protected from outbreaks of illnesses
- Infection-protected from unstable magnesium gas, explosively released
- One madame stifling a Parisian male — not susceptible
- ... getting protected from the upsetting note attached to the decorated menu
- Unlikely to be affected, I take millions to a French one
- One taking a French female without gentlemen is secure
Buddy explains!

The straight part
We know that "so complaint impossible" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case so complaint impossible = immune.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 IMMUNE mean?
IMMUNE noun- A person who is not susceptible to infection by a particular disease
- To make immune.
- (usually with "from") Exempt; not subject to.
- (usually with "to") Protected by inoculation, or due to innate resistance to pathogens.
- (by extension) Not vulnerable.
- Of or pertaining to the immune system.