New leader of Labour party is insignificant (6)
I believe the answer is:
paltry
'insignificant' is the definition.
(thesaurus)
'new leader of labour party' is the wordplay.
'new' indicates anagramming the letters.
'leader of' indicates taking the first letters.
The initial letter of 'labour' is 'l'.
'l'+'party'='lparty'
'lparty' with letters rearranged gives 'PALTRY'.
'is' is the link.
(Other definitions for paltry that I've seen before include "Insignificant, trifling" , "Meagre, mean" , "Worthless and trifling" , "Minor, insignificant" , "Petty - base" .)