Dad goes up to see doctor with self-possession (6)
I believe the answer is:
aplomb
'self-possession' is the definition.
('aplomb' can be a synonym of 'self-possession')
'dad goes up to see doctor' is the wordplay.
'dad' becomes 'pa' ('pa' can be a synonym of 'dad').
'goes up' says the letters should be written backwards.
'to see' becomes 'lo' (archaic word meaning 'look!').
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'pa' written backwards gives 'ap'.
'ap'+'lo'+'mb'='APLOMB'
'with' is the link.
(Other definitions for aplomb that I've seen before include "Self-possession - coolness" , "Self confidence" , "Calm self-assurance and poise" , "Dignified self-confidence" , "Self-satisfied dignity, complacency" .)