Hotel where there may be pie? But without fat (6)
I believe the answer is:
skinny
'without fat' is the definition.
'hotel where there may be pie?' is the wordplay.
I cannot quite see how this works, but
'hotel' could be 'inn' (inn is a kind of hotel) and 'inn' is found in the answer.
The remaining letters 'sky' is a valid word which might be clued in a way I don't see.
This may be the basis of clue (or it may be nonsense).
'but' is the link.
(Other definitions for skinny that I've seen before include "Scrawny, underweight" , "Lean" , "Not very well-built" , "Lacking food" , "Low-calorie white coffee -- sent any kilt (anag)" .)