Son, in part, runs ordinary restaurant (6)
I believe the answer is:
bistro
'restaurant' is the definition.
(bistro is a kind of restaurant)
'son in part runs ordinary' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'in' indicates putting letters inside.
'part' becomes 'bit' (both mean a piece of something).
'runs' becomes 'r' (cricket abbreviation).
'ordinary' becomes 'O' (abbreviation e.g. O-Levels).
's' put inside 'bit' is 'bist'.
'bist'+'r'+'o'='BISTRO'
(Other definitions for bistro that I've seen before include "Intimate eatery" , "'Small, inexpensive restaurant (6)'" , "Coming out of restaurant" , "somewhere to eat" , "Small informal French cafi" .)