Eccentric, Beryl? Hope that's exaggeration (9)
I believe the answer is:
hyperbole
'exaggeration' is the definition.
(I know that exaggeration can be written as hyperbole)
'eccentric beryl? hope' is the wordplay.
'eccentric' indicates an anagram.
'beryl'+'hope'='berylhope'
'berylhope' with letters rearranged gives 'HYPERBOLE'.
'that's' acts as a link.
(Other definitions for hyperbole that I've seen before include "Exaggerated claims" , "Deliberate exaggeration used for effect" , "not to be taken literally" , "Exaggerated language, not meant literally" , "The use of exaggeration for effect" .)