Greasy old cycle is regularly brought back (4)
I believe the answer is:
oily
'greasy' is the definition.
(synonyms)
'old cycle is regularly brought back' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'brought back' is a reversal indicator.
'cycle'+'is'='cycleis'
The alternate letters of 'cycleis' are 'yli'.
'yli' written backwards gives 'ily'.
'o'+'ily'='OILY'
(Other definitions for oily that I've seen before include "Covered in lubricant" , "Oleaginous" , "Smooth; like lubricant" , "Viscous" , "Smoothly ingratiating" .)