The most common and most likely answer to this crossword clue is the 5 plus 6 letter word OLIVE BRANCH
I've seen this crossword clue in The Times
O
L
I
V
E
B
R
A
N
C
H
More clues leading to the result OLIVE BRANCH
- Girl born on farm makes conciliatory gesture
- None, as it happens, refuse church’s conciliatory offer
- Peace offering from old boy in possession of working farm
- Oscar’s current department makes peace offering
- Pacific offer from section of Green Party?
- Berlin havoc got round with offer of reconciliation
- Peace offering from Green Wing?
- Peace symbol round active department
- Peace offering from bachelor in 7 around 5
- Shocked Ivor with Blanche’s offer of reconciliation
Buddy explains!

The straight part
We know that "conciliatory offer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case conciliatory offer = olive branch.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 OLIVE BRANCH mean?
OLIVE BRANCH verb- To extend an olive branch; to make a peace offering; to attempt to restore peaceful relations.