Former prime minister has argument in airport (8)
I believe the answer is:
heathrow
'airport' is the definition.
(London airport)
'former prime minister has argument' is the wordplay.
'former prime minister' becomes 'Heath' (Ted Heath, UK prime minister 1970-74).
'has' says to put letters next to each other.
'argument' becomes 'row' (to row is to argue).
'heath'+'row'='HEATHROW'
'in' acts as a link.
(Other definitions for heathrow that I've seen before include "lots of movement through the air here" , "London's main airport" , "London airport" , "site for airport" , "our counterpart of Charles de Gaulle" .)