Excitedly greet clan figure (9)
I believe the answer is:
rectangle
'figure' is the definition.
(rectangle is a kind of figure)
'excitedly greet clan' is the wordplay.
'excitedly' is an anagram indicator (letters excited or stimulated into a new form).
'greet'+'clan'='greetclan'
'greetclan' is an anagram of 'RECTANGLE'.
(Other definitions for rectangle that I've seen before include "Oblong" , "Quadrilateral" , "Geometric figure with four right angles, not square" , "Four sides involved in this" , "Four-sided figure" .)