Cryptic crossword clue
A bighead lacking any aspiration, the man was duly rewarded with time 7

The most common and most likely answer to this crossword clue is the 7 letter word EGOTIST

I've seen this crossword clue in Independent
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The cryptic/wordplay part
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This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
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What does EGOTIST mean?

EGOTIST noun
  1. A person who talks excessively about himself or herself.
  2. A person who believes in his or her own importance or superiority.
  3. An egoist.

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