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' indicates an anagram.
'around' is an insertion indicator.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'year' becomes 'y'.
'hope' is an anagram of '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" .)