The most common and most likely answer to this crossword clue is the 7 letter word OVERTLY
I've seen this crossword clue in The Sunday Telegraph
O
V
E
R
T
L
Y
More clues leading to the result OVERTLY
- 'eavenly sandwiches green, clearly!
- Holding bottom of hat, too obviously
- Devout Cockney crossing green in full view
- Obviously young support liberal revolt
- Revolt affected yobbos’ leader, clearly
- Surplus tax changing hands in public
- Too full of themselves at first, for all to see
- Dismissing head, secretly or in public?
- Up in the air, cross, having taken time for female in public
- Excessively protecting Tory leader in public
Buddy explains!

The straight part
We know that "Excessively" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case excessively = overtly.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 OVERTLY mean?
OVERTLY adverb- In an overt manner; publicly; openly.