Father's got up in posh style to see a poetess (6)
I believe the answer is:
sappho
'a poetess' is the definition.
(I have seen 'Greek poetess' mean 'sappho' so perhaps 'poetess' could also mean 'sappho')
'father's got up in posh style' is the wordplay.
'father' becomes 'pa' (pa can mean dad or father).
'got up' says the letters should be written in reverse.
'in' is an insertion indicator.
'style' indicates an anagram (style can mean to shape or design).
'pa' written backwards gives 'ap'.
'posh' is an anagram of 'spho'.
'ap' placed inside 'spho' is 'SAPPHO'.
'to see' acts as a link.
(Other definitions for sappho that I've seen before include "Ancient Greek poet of Lesbos" , "Pa hops about Greek poet from Lesbos" , "Greek lyric poetess" , "Greek lyric poet of Lesbos" , "Greek poetess; has pop (anag.)" .)