Unsympathetic detectives asked to support sick (3-8)
I believe the answer is:
ill-disposed
'unsympathetic' is the definition.
(I've seen this before)
'detectives asked to support sick' is the wordplay.
'detectives' becomes 'dis' (Detective Inspectors, DIs).
'asked' becomes 'posed' ('pose' can be a synonym of 'ask'**).
'to support' says to put letters next to each other (in a down clue, some letters hold others up).
'sick' becomes 'ill' ('ill' can be a synonym of 'sick').
'dis'+'posed'='disposed'
'disposed' after 'ill' is 'ILL-DISPOSED'.
(Another definition for ill-disposed that I've seen is " Unfriendly, unsympathetic".)