Tear off to be entertained by thin relation (5-4)
I believe the answer is:
great-aunt
'relation' is the definition.
(great-aunt is a kind of relation)
'tear off to be entertained by thin' is the subsidiary indication.
'off' is an anagram indicator.
'to be entertained by' means one lot of letters goes inside another (I've seen this in other clues).
'thin' becomes 'gaunt' ('gaunt' can be similar in meaning to 'thin'**).
'tear' anagrammed gives 'reat'.
'reat' going into 'gaunt' is 'greataunt'.
(Another definition for great-aunt that I've seen is " Tag nature (anag) - relative".)