Susie or Dicky in grave (7)
I believe the answer is:
serious
'grave' is the definition.
(I know that grave can be written as serious)
'susie or dicky' is the wordplay.
'dicky' is an anagram indicator (dicky can mean ill or non-functioning).
'susie'+'or'='susieor'
'susieor' anagrammed gives 'SERIOUS'.
'in' acts as a link.
(Other definitions for serious that I've seen before include "Important -- grave" , "Important - solemn" , "Earnest, sincere" , "Solemn, thoughtful" , "Earnest - important" .)