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' indicates putting letters inside.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'year' becomes 'y'.
'hope' with letters rearranged gives 'phoe'.
'phoe' placed 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" .)