The most common and most likely answer to this crossword clue is the 13 letter word EXHIBITIONIST
I've seen this crossword clue in Independent
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More clues leading to the result EXHIBITIONIST
Buddy explains!
The straight part
We know that "I show off" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case i show off = exhibitionist.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.
Crossword Answer definitions
EXHIBITIONIST noun- A student at secondary school or university who has been awarded an exhibition. The exhibition usually involves a financial prize and may include the right to wear a distinctive gown, especially at the University of Oxford.
- One who attempts to draw attention to himself or herself by his or her behaviour.
- One who exposes his or her genitalia (or female nipples) in public.
- Compulsively seeking attention