Keep on turning up at pub, disheartened (6)
I believe the answer is:
retain
'keep' is the definition.
(I know that retain is a more specific form of keep)
'on turning up at pub disheartened' is the wordplay.
'on' becomes 're' (regarding).
'turning up' says the letters should be written in reverse.
'pub' becomes 'inn' (an inn is a type of pub).
'disheartened' means to remove the middle letters (the middle or heart is removed).
'inn' with its centre removed is 'in'.
'at' reversed gives 'ta'.
're'+'ta'+'in'='RETAIN'
(Other definitions for retain that I've seen before include "Keep; remember" , "Save" , "Not relinquish" , "Keep in Tirane" , "Hold on to or employ counsel" .)