Contact the Guardian about job centre that's unfeeling (7)
I believe the answer is:
callous
'unfeeling' is the definition.
(synonyms)
'contact the guardian about job centre' is the wordplay.
'contact' becomes 'call'.
'the guardian' becomes 'us' (the crossword setter and their Guardian colleagues).
'about' says to put letters next to each other.
'centre' indicates the central letters.
The central letter of 'job' is 'o'.
'us' after 'o' is 'ous'.
'call'+'ous'='CALLOUS'
'that's' is the link.
(Other definitions for callous that I've seen before include "Not feeling" , "Cruel and unfeeling" , "Cruelly unfeeling" , "Hard-hearted" , "Emotionally hardened" .)