The heartless rich I suspect to be more irritating (7)
I believe the answer is:
itchier
'be more irritating' is the definition.
(I've seen this before)
'the heartless rich i suspect' is the wordplay.
'heartless' means to remove the middle letters.
'suspect' indicates an anagram.
'the' with its middle taken out is 'te'.
'te'+'rich'+'i'='terichi'
'terichi' with letters rearranged gives 'ITCHIER'.
'to' is the link.
(Other definitions for itchier that I've seen before include "Comparatively irritating" , "More fidgety, more restless" , "More ticklish" , "burning intensely!" , "more aggravating" .)