That heartless Etonian out to get recognition (9)
I believe the answer is:
attention
'recognition' is the definition.
(thesaurus)
'that heartless etonian out' is the wordplay.
'heartless' means to remove the middle letters.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'that' with its centre removed is 'tt'.
'tt'+'etonian'='ttetonian'
'ttetonian' is an anagram of 'ATTENTION'.
'to get' is the link.
(Other definitions for attention that I've seen before include "Applicaton, concentration" , "Vigilance; care" , "careful thought" , "Awareness - regard" , "Special care, soldier's position" .)