The most common and most likely answer to this crossword clue is the 4 plus 5 letter word TALL ORDER
I've seen this crossword clue in The Daily Telegraph
T
A
L
L
O
R
D
E
R
More clues leading to the result TALL ORDER
- Demand for giraffes perhaps that is hard to fulfil?
- Big ask, delivery of giraffe perhaps?
- . Difficult task of monks who need a high ceiling?
- Coffee requested in twelve- ounce cup? That’s unlikely to happen
- Big ask short term saves shaky dollar
- Group of animals including giraffes perhaps facing tough task
- Incredible to authorise an unreasonably difficult assignment
- Formidable task in directive from on high?
- Band of Brothers extended quite a challenge
- Write story about my Romeo – that’s a demanding task
Buddy explains!
The straight part
We know that "Difficult assignment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case difficult assignment = tall order.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.