Pop up and see doctor: being collected (6)
I believe the answer is:
aplomb
'being collected' is the definition.
(aplomb is being collected or poised)
'pop up and see doctor' is the wordplay.
'pop' becomes 'pa' (both can mean father).
'up' is a reversal indicator (in down clue: letters go upwards).
'and' says to put letters next to each other.
'see' becomes 'lo' (archaic word meaning 'look!').
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'pa' reversed gives 'ap'.
'ap'+'lo'+'mb'='APLOMB'
(Other definitions for aplomb that I've seen before include "Self-possession, assurance" , "Nonchalant confidence" , "Self-confidence, assurance" , "Cool self-assurance" , "Great coolness and composure under strain" .)