Thus identify describing newspaper’s vulnerability (4,4)
I believe the answer is:
soft spot
'vulnerability' is the definition.
(thesaurus)
'thus identify describing newspaper's' is the wordplay.
'thus' becomes 'so' (synonyms).
'identify' becomes 'spot' (I've seen this before).
'describing' is an insertion indicator (describe can mean to form the outline of).
'newspaper' becomes 'ft' (Financial Times newspaper).
'so'+'spot'='sospot'
'sospot' placed around 'ft' is 'SOFT SPOT'.
(Other definitions for soft spot that I've seen before include "showing fondness" , "Sentimental affection" , "Emotional susceptibility" , "Affectionate weakness for (someone/something)" , "Sentimental fondness" .)