Conservative going kind of pink, concerned with speech (4)
I believe the answer is:
oral
'speech' is the definition.
(oral means relating to speech)
'conservative going kind of pink' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'going' indicates named letters should be taken away.
'kind of pink' becomes 'coral'.
'coral' with 'c' taken out is 'ORAL'.
'concerned with' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for oral that I've seen before include "Ant; tourist (dial.)" , "Viva voce" , "Vocal test" , "Relating to the mouth - exam" , "Using speech rather than writing" .)