Politician first on right to chase the money (8)
I believe the answer is:
centrist
'politician' is the definition.
(I have seen 'Moderate politician ' mean 'centrist' so perhaps 'politician' could also mean 'centrist')
'first on right to chase the money' is the wordplay.
I cannot quite see how this works, but
'first' could be 'ist' (ist resembles 1st) and 'ist' is found within the answer.
'right' could be 'r' (abbreviation) and 'r' is located in the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is present in the answer.
'money' could be 'c' and 'c' is found within the answer.
The remaining letters 'en' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
(Other definitions for centrist that I've seen before include "Politician who takes middle-of-the-road position" , "Person who takes a middle-of-the-road political position" , "A middle-of-the-road person in politics" , "One taking the middle ground" , "Moderate politician" .)