Angrily cancel Ken, rejecting one new piece of jewellery (8)
I believe the answer is:
necklace
'piece of jewellery' is the definition.
(I've seen this before)
'angrily cancel ken rejecting one new' is the wordplay.
'angrily' is an anagram indicator (I've seen this in other clues).
'rejecting' is a deletion indicator.
'one new' becomes 'n' (common abbreviation eg NT for New Testament).
'cancel'+'ken'='cancelken'
'cancelken' with 'n' taken away is 'cacelken'.
'cacelken' is an anagram of 'NECKLACE'.
(Other definitions for necklace that I've seen before include "Ornamental string" , "Ornamental chain or cord" , "Eg, a choker" , "responsible for murder in South Africa" , "decorative band" .)