The most common and most likely answer to this crossword clue is the 6 letter word CONVEX
I've seen this crossword clue in Independent
C
O
N
V
E
X
More clues leading to the result CONVEX
- Trick with needle to get swelling out
- Curved kind of oven found in empty chateaux
- Rounded channel turning axis through 90 degrees
- Outgoing figure claiming virgin’s first kiss
- Many aboard worry it’s bulging outwards
- Rounded firm new cheese off
- Transfer group to protect Navy
- Cheat and nag for a mirror
- Prominent criminal is over trouble
Buddy explains!

The straight part
We know that "Outgoing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case outgoing = convex.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 CONVEX mean?
CONVEX noun- Any convex body or surface.
- Curved or bowed outward like the outside of a bowl or sphere or circle
- (of a set in Euclidean space) arranged such that for any two points in the set, a straight line between the two points is contained within the set.
- (of a polygon) having no internal angles greater than 180 degrees.
- (of a real-valued function on the reals) having an epigraph which is a convex set.