Covert behaviour's appropriate, though heartless (7)
I believe the answer is:
stealth
'covert behaviour's' is the definition.
'appropriate though heartless' is the wordplay.
'appropriate' becomes 'steal' (I've seen this before).
'heartless' suggests removing the centre.
'though' with its centre removed is 'th'.
'steal'+'th'='STEALTH'
(Other definitions for stealth that I've seen before include "By which taxes go up" , "Quiet or secret way of behaviour" , "word to define secrecy" , "Secretiveness, furtiveness" , "Halt set in furtive manner" .)