The most common and most likely answer to this crossword clue is the 6 letter word ROOTED
I've seen this crossword clue in The Guardian
R
O
O
T
E
D
Buddy explains!
The straight part
We know that "Offered support/established" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case offered support/established = rooted.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 ROOTED mean?
ROOTED verb- To grow roots; to enter the earth, as roots; to take root and begin to grow.
- To prepare, oversee, or otherwise cause the rooting of cuttings
- To be firmly fixed; to be established.
- To get root or priviledged access on a computer system or mobile phone, often through bypassing some security mechanism.
- To turn up or dig with the snout.
- (by extension) To seek favour or advancement by low arts or grovelling servility; to fawn.
- To rummage; to search as if by digging in soil.
- To root out; to abolish.
- To have sexual intercourse.
- (with "for" or "on") To cheer (on); to show support (for) and hope for the success of. (See root for.)
- Having roots, or certain type of roots.
- Fixed in one position; immobile; unable to move.
- Ingrained, as through repeated use; entrenched; habitual or instinctive.
- (usually with "in") Having a basic or fundamental connection (to a thing); based, originating (from).
- (of a tree or graph) Having a root.
- In trouble or in strife, screwed.
- Broken, damaged, non-functional.
- Having a root (superuser) account that has been compromised.