Indiscreet, interminably rude and sick at heart (9)
I believe the answer is:
impolitic
'indiscreet' is the definition.
(thesaurus)
'interminably rude and sick at heart' is the wordplay.
'interminably' means to remove the last letter.
'rude' becomes 'impolite' ('impolite' can be similar in meaning to 'rude').
'and' means one lot of letters go next to another.
'sick at heart' becomes 'ic' (I can't justify this - if you can you should give a lot more credence to this answer).
'impolite' with its last letter taken off is 'impolit'.
'impolit'+'ic'='IMPOLITIC'
(Other definitions for impolitic that I've seen before include "Lacking prudence, unwise" , "Not prudent" , "Inexpedient" , "Ill-advised" .)