Member of nonet in desert in outskirts of El Paso (5)
I believe the answer is:
erato
'member of nonet' is the definition.
(one of the nine muses - a nonet is a group of nine)
'desert in outskirts of el paso' is the wordplay.
I cannot quite understand how this works, but
'desert' could be 'rat' (abandon treacherously) and 'rat' is located in the answer.
The remaining letters 'eo' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
'in' is the link.
(Other definitions for erato that I've seen before include "Poet's inspiration" , "Who may have inspired poetry" , "goddess" , "Muse of lyric love-poetry" , "One inspiring" .)