The most common and most likely answer to this crossword clue is the 7 letter word REVERED
I've seen this crossword clue in The Sunday Telegraph
R
E
V
E
R
E
D
More clues leading to the result REVERED
Buddy explains!

The straight part
We know that "greatly admired" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case greatly admired = revered.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 REVERED mean?
REVERED verb- To regard someone or something with great awe or devotion.
- To honour in a form lesser than worship, e.g. a saint, or an idol
- Respected or given reverence