Conservative keeps calm, with hearts sinking (3,6)
I believe the answer is:
old school
'conservative' is the definition.
(thesaurus)
I don't understand the rest of the clue.
(Other definitions for old school that I've seen before include "In Westminster" , "Group favouring conservative practices" , "group that has no small fry in it?" , "Conservative thinkers" , "a bunch of conservative types" .)