The most common and most likely answer to this crossword clue is the 8 letter word ADOPTION
I've seen this crossword clue in The Daily Telegraph
A
D
O
P
T
I
O
N
More clues leading to the result ADOPTION
- Taking in a child — a daughter by choice
- Taking on a commercial possibility
- Taking on a lecturer without work — half time
- A key choice, fostering
- Taking up dubious point made by a party
- Approval of god usurped by priest in worship
- Acceptance of taking our time over choice
- Backing fixed to an iPod
- Notice work getting into shape for a takeover
- Taking trouble to point out
Buddy explains!

The straight part
We know that "child-rearing arrangement" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case child-rearing arrangement = adoption.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 ADOPTION mean?
ADOPTION noun- The act of adopting.
- The state of being adopted; the acceptance of a child of other parents as if he or she were one's own child.
- Admission to an institution, for example a hospital, clinic, mental asylum.
- The choosing and making that to be one's own which originally was not so; acceptance
- Transfer between an old system to another (usually better) system.
- An act of divine grace by which the redeemed in Christ are admitted to the privileges of the sons of God.
- Ten consecutive wins against an opponent.