Not quite slow or fast (4)
I believe the answer is:
lent
'fast' is the definition.
(I've seen this before)
'not quite slow' is the wordplay.
'not quite' means to remove the last letter.
'slow' becomes 'lento' ('lento' can be similar in meaning to 'slow').
'lento' with its last letter taken off is 'LENT'.
'or' is the link.
(Other definitions for lent that I've seen before include "days before Easter" , "Period of penance" , "Christian penitential season" , "Gave for a limited period" , "Period of fasting" .)