The most common and most likely answer to this crossword clue is the 7 letter word CABOOSE
C
A
B
O
O
S
E
Buddy explains!

The straight part
We know that "American at the rear" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case american at the rear = caboose.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 CABOOSE mean?
CABOOSE noun- A small galley or cookhouse on the deck of a small vessel.
- A small sand-filled container used as an oven on board ship.
- The last car on a freight train, having cooking and sleeping facilities for the crew; a guard’s van.
- Buttocks
- The person or team in last place.
- A youngest child who is born after a big gap in time.