Repeatedly say nothing about heartless executive? How exasperating! (6)

'how exasperating' is the definition.
(expression of exasperation)

'repeatedly say nothing about heartless executive?' is the wordplay.
'repeatedly' shows that letters should be duplicated.
'say nothing' becomes 'sh' ('sh' is said to tell someone to say nothing).
'about' is an insertion indicator.
'heartless' says to hollow out the word (remove centre letters).
'executive' with its centre removed is 'ee'.
'sh' doubled is 'shsh'.
'shsh' placed around 'ee' is 'SHEESH'.