One in favour of exterminating Doctor Who (5)
I believe the answer is:
dalek
'one in favour of exterminating' is the definition.
I don't know anything about this answer so I cannot tell 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" .)