Fibre Formula 1 regret (8)
I believe the answer is:
filament
'fibre' is the definition.
(filament is a kind of fibre)
'formula 1 regret' is the wordplay.
'formula 1' becomes 'fi' (resembles F1).
'regret' becomes 'lament' ('lament' can be a synonym of 'regret').
'fi'+'lament'='FILAMENT'
(Other definitions for filament that I've seen before include "'Thin wire, in a bulb say (8)'" , "Thread-like object" , "It glows in a light bulb" , "Strand" , "Fine thread" .)