Relative starts to do elegant swan impression (9)
I believe the answer is:
dependent
'relative' is the definition.
(thesaurus)
'starts to do elegant swan impression' is the wordplay.
'starts to' indicates taking the first letters.
'swan' becomes 'pen' (pen is a kind of swan).
'impression' becomes 'dent' (dent is a kind of impression).
The first letters of 'do elegant' is 'de'.
'de'+'pen'+'dent'='DEPENDENT'
(Other definitions for dependent that I've seen before include "Relying/contingent (on)" , "Reliant" , "Subject" .)