One in transport mum uses getting dad to Paris (5)
I believe the answer is:
priam
'dad to paris' is the definition.
(father of Paris in Greek myth)
'one in transport mum uses' is the wordplay.
'one' becomes 'i' (Roman numeral**).
'in' is an insertion indicator.
'transport mum uses' becomes 'pram'.
'i' placed within 'pram' is 'PRIAM'.
'getting' acts as a link.
(Other definitions for priam that I've seen before include "Ruler of Troy" , "Trojan king" , "The last king of Troy, in Greek mythology" , "Old king" , "Old man of Paris" .)