Inclination to drill until Thursday (4)
I believe the answer is:
tilt
'inclination' is the definition.
(I know that inclination can be written as tilt)
'to drill until thursday' is the wordplay.
'to drill' indicates a hidden word (the answer drills into the clue).
'TILT' is hidden in the letters of 'until thursday'.
(Other definitions for tilt that I've seen before include "Lean to one side" , "Inclination, joust" , "Heel over" , "Be inclined" , "Lean sideways" .)