A pedantic air I contrived as a medical specialist (13)
I believe the answer is:
paediatrician
'a medical specialist' is the definition.
(paediatrician is a kind of medical specialist)
'a pedantic air i contrived' is the wordplay.
'contrived' indicates anagramming the letters.
'a'+'pedantic'+'air'+'i'='apedanticairi'
'apedanticairi' with letters rearranged gives 'PAEDIATRICIAN'.
'as' is the link.
(Other definitions for paediatrician that I've seen before include "Child doctor" , "Child's doctor" , "Specialist in children and their diseases" , "Specialist in treating children" .)