Do nothing, say, about a generation without heart (8)
I believe the answer is:
stagnate
'do nothing' is the definition.
(thesaurus)
'say about a generation without heart' is the wordplay.
'say' becomes 'state' ('state' can be a synonym of 'say'**).
'about' is an insertion indicator.
'without heart' suggests removing the centre.
'generation' with its centre taken out is 'gn'.
'a'+'gn'='agn'
'state' placed around 'agn' is 'STAGNATE'.
(Other definitions for stagnate that I've seen before include "resemble pond water?" , "Cease to flow and become smelly" , "Become still and stale, pond or people (8)" , "Become inactive (and malodorous)" , "Stop shifting" .)