The most common and most likely answer to this crossword clue is the 7 letter word DOROTHY
I've seen this crossword clue in The Guardian
D
O
R
O
T
H
Y
More clues leading to the result DOROTHY
- Too dry and hot unfortunately for visitor to Oz
- Parker cooked hot fish outside
- Girl vaguely hot having eaten fish? The opposite
- Name fish with unusually hot stuffing
- Hot springs with fish circling one of 5D’s troupe
- Peculiar door next to your heroine in Oz
- Woman specially fitted to dry Oscar Hammerstein’s head
- Make elevator’s last operator your fantasy girl?
Buddy explains!

The straight part
We know that "Parker" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case parker = dorothy.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.