Father's coat always ragged ultimately and threadbare (6)
I believe the answer is:
frayed
'threadbare' is the definition.
(thesaurus)
'father's coat always ragged ultimately' is the wordplay.
'coat' means to remove the middle letters (only the letters which coat the word are used).
'always' becomes 'aye' (archaic term for 'always').
'ultimately' says to take the final letters.
'father' with its centre taken out is 'fr'.
The final letter of 'ragged' is 'd'.
'fr'+'aye'+'d'='FRAYED'
'and' acts as a link.
(Other definitions for frayed that I've seen before include "in rough condition" , "Tattered and worn at edges" , "Became strained" , "Worn away at the edges" , "Ragged at the edges" .)