Father with posh girl is thrifty (6)
I believe the answer is:
frugal
'thrifty' is the definition.
('frugal' can be similar in meaning to 'thrifty')
'father with posh girl' is the wordplay.
'father' becomes 'fr'.
'with' means one lot of letters go next to another.
'posh' becomes 'u' (abbreviation for upper-class - opposite to non-u).
'girl' becomes 'gal' ('gal' can be a synonym of 'girl'**).
'fr'+'u'+'gal'='FRUGAL'
'is' is the link.
(Other definitions for frugal that I've seen before include "Sparing, avoiding waste," , "Economical and careful" , "Economical, avoiding waste" , "not expensive" , "Sparing, meagre" .)