Dispirited, having no inventory? (8)
I believe the answer is:
listless
'dispirited' is the definition.
(I know that dispirited can be written as listless)
'no inventory' is the wordplay.
I cannot quite see how this works, but
'inventory' could be 'list' (I've seen this before) and 'list' is found within the answer.
The remaining letters 'less' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
'having' is the link.
(Other definitions for listless that I've seen before include "Languid - apathetic" , "Low-spirited" , "Tells sis to be lacking in energy" , "Lacking zest or enthusiasm" , "Without energy or vitality" .)