Shape is round, involving a square (8)
I believe the answer is:
dinosaur
'square' is the definition.
(both can mean an old-fashioned person)
'shape is round involving a' is the wordplay.
'shape' is an anagram indicator.
'involving' is an insertion indicator.
'is'+'round'='isround'
'isround' is an anagram of 'dinosur'.
'dinosur' going around 'a' is 'DINOSAUR'.
(Other definitions for dinosaur that I've seen before include "Eg, triceratops" , "Extinct monster like Barney, children's TV pal" , "Creature no longer" , "Reptile is around, not really" , "I adorn US with this old creature" .)