The most common and most likely answer to this crossword clue is the 8 letter word NON-IRON
I've seen this crossword clue in The Guardian
N
O
N
-
I
R
O
N
More clues leading to the result NON-IRON
Buddy explains!

The straight part
We know that "kind of shirt?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kind of shirt? = non-iron.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 NON-IRON mean?
NON-IRON adjective- That does not need ironing.