Father is holding learners responsible for unnecessary embellishments (6)
I believe the answer is:
frills
'unnecessary embellishments' is the definition.
(a frill is an embellishment)
'father is holding learners' is the wordplay.
'father' becomes 'fr' (abbreviation as in a priest's title).
'holding' indicates putting letters inside.
'learners' becomes 'LL' (the abbreviation for learner driver written twice).
'is' enclosing 'll' is 'ills'.
'fr'+'ills'='FRILLS'
'responsible for' acts as a link.
(Other definitions for frills that I've seen before include "Gatherings" , "Strips of garment trimming or unnecessary extras" , "Basically there's none of these!" , "Ruffles and flounces" , "absent from thrift shops" .)