Inclination to cheat at bagatelle (4)
I believe the answer is:
tilt
'inclination' is the definition.
(synonyms)
'to cheat at bagatelle' is the wordplay.
I cannot quite see how this works, but
'to' could be 'til' (I've seen this in another clue) and 'til' is found in the answer.
A single letter 't' remains which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for tilt that I've seen before include "Move into a sloping position, say a lance" , "Tip to one side" , "Engage in a medieval joust - lean" , "Incline, slant" , "Thrust with lance, like Don Quixote at windmills" .)