Notice the heartless miser troubled in period before Christmas (13)
I believe the answer is:
advertisement
'notice' is the definition.
(I've seen this before)
'the heartless miser troubled in period before christmas' is the wordplay.
'heartless' means to remove the middle letters.
'troubled' is an anagram indicator.
'in' is an insertion indicator.
'period before christmas' becomes 'advent' (advent is the period leading up to Christmas Day).
'the' with its middle taken out is 'te'.
'te'+'miser'='temiser'
'temiser' is an anagram of 'ertisem'.
'ertisem' put inside 'advent' is 'ADVERTISEMENT'.
(Other definitions for advertisement that I've seen before include "Commercial promotion" , "Publicity announcement" , "Notice - commercial" , "plug" , "Placard" .)