The most common and most likely answer to this crossword clue is the 10 letter word ENTHRALLED
I've seen this crossword clue in The Times
E
N
T
H
R
A
L
L
E
D
Buddy explains!

The straight part
We know that "Transported" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case transported = enthralled.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 ENTHRALLED mean?
ENTHRALLED verb- To hold spellbound; to bewitch, charm or captivate.
- To make subservient; to enslave or subjugate.
- Fascinated; captivated.