The most common and most likely answer to this crossword clue is the 4 plus 4 letter word TRUE BLUE
I've seen this crossword clue in The Times
T
R
U
E
B
L
U
E
More clues leading to the result TRUE BLUE
- Staunch supporter certain at heart to regret waste
- A Spandau Ballet song, a Joni Mitchell song and a Madonna song
- Very faithful type not lying down
- Loyal Tory Unionist, twice and thrice over
- Awful trouble with EU showing no love for diehard Tory?
- Staunch Conservative showing regret, depressed after time
- A person who always votes Conservative must be really sad
- Staunchly loyal Unions individual involved in bet
- Ceasefire caught out unhappy supporter
- Staunch Tory regularly tortures police officer
Buddy explains!

The straight part
We know that "Staunch supporter" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case staunch supporter = true blue.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 TRUE BLUE mean?
TRUE BLUE adjective- Steadfastly loyal or faithful, unwavering in loyalty.
- Authentic, undoubtedly true; honest.