Authority to apply pressure internally (6)
I believe the answer is:
expert
'authority' is the definition.
(I've seen this before)
'apply pressure internally' is the wordplay.
'apply' becomes 'exert' (exerting is a kind of applying**).
'pressure' becomes 'p' (abbreviation).
'internally' is an insertion indicator.
'exert' going around 'p' is 'EXPERT'.
'to' acts as a link.
(Other definitions for expert that I've seen before include "Pro" , "Person with great knowledge or skill, specialist" , "At the right moment" , "Having specialised knowledge" , "Dab hand" .)