False hope develops around New Year (6)
I believe the answer is:
phoney
'false' is the definition.
(thesaurus)
'hope develops around new year' is the wordplay.
'develops' is an anagram indicator.
'around' is an insertion indicator.
'new' becomes 'n' (abbreviation as in New Testament NT).
'year' becomes 'y'.
'hope' anagrammed gives 'phoe'.
'phoe' going around 'n' is 'phone'.
'phone'+'y'='PHONEY'
(Other definitions for phoney that I've seen before include "Sham, not genuine or sincere" , "Not genuine, insincere" , "Fraud" , "Fraudulent" , "Fake, misleading" .)