The most common and most likely answer to this crossword clue is the 3 plus 4 letter word HIS NIBS
I've seen this crossword clue in The Daily Telegraph
H
I
S
N
I
B
S
More clues leading to the result HIS NIBS
Buddy explains!

The straight part
We know that "Ironic title" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ironic title = his nibs.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.