One in favour of exterminating Doctor Who (5)
I believe the answer is:
dalek
'one in favour of exterminating' is the definition.
I know nothing about this answer so I can't judge whether it can be defined by this definition.
'doctor who' is the wordplay.
'doctor' becomes 'd' (eg in PhD, Doctor of Philosophy).
'who' becomes 'alek' (I can't explain this - if you can you should give a lot more credence to this answer).
'd'+'alek'='DALEK'
Can you help me to learn more?
(Other definitions for dalek that I've seen before include "Who does one want to kill" , "Foe of Doctor Who" , "Alien creation" , "Dr Who's alien robot" , "mechanical creature" .)