Presence of this person beset by anger (6)
I believe the answer is:
wraith
'presence' is the definition.
(I've seen this before)
'this person beset by anger' is the wordplay.
'this person' becomes 'i'.
'beset by' indicates putting letters inside ('beset' could historically mean 'cover').
'anger' becomes 'wrath' (wrath is a kind of anger).
'i' inserted into 'wrath' is 'WRAITH'.
'of' is the link.
(Other definitions for wraith that I've seen before include "Wrath I directed at spirit" , "Ghostly apparition" , "Deathly apparition" , "Making an emotional appeal" , "Ghost-like apparition" .)