The most common and most likely answer to this crossword clue is the 7 letter word PHOENIX
I've seen this crossword clue in The Times
P
H
O
E
N
I
X
More clues leading to the result PHOENIX
- With mobile phone I’ll get by in desert city
- Hope to organise veto for US city
- Mythical bird? It’s found in Arizona
- Fabulous bird park in Dublin
- Before first kiss, nervously phone fabulous bird
- With one hip broken, cross 23?
- It symbolises rebirth of hope in troubled times
- Mythical creature somewhere in Arizona
- Spooner’s joint repair as a symbol of new life
- Stupidly hope for nothing from the Firebird
Buddy explains!

The straight part
We know that "desert city" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case desert city = phoenix.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 PHOENIX mean?
PHOENIX noun- A mythological bird, said to be the only one of its kind, which lives for 500 years and then dies by burning to ashes on a pyre of its own making, ignited by the sun. It then arises anew from the ashes.
- Anything that is reborn after apparently being destroyed.
- A mythological Chinese chimerical bird whose physical body symbolizes the six celestial bodies.
- A Greek silver coin used briefly from 1828 to 1832, divided into 100 lepta.