Base and vicious, determined to annoy (7)
I believe the answer is:
bedevil
'to annoy' is the definition.
(I know that bedevil is a more specific form of the action beset)
'base and vicious' is the wordplay.
'base' becomes 'bed' (both can mean the bottom of something).
'and' is a charade indicator (letters next to each other).
'vicious' becomes 'evil' (synonyms).
'bed'+'evil'='BEDEVIL'
'determined' is the link.
This may not be right. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for bedevil that I've seen before include "Cause continual difficulties" , "Dog" , "Throw into confusion" , "Afflict" , "torment" .)