Her cats regularly departed after snake's appearance (6)
I believe the answer is:
aspect
'appearance' is the definition.
(aspect is a kind of appearance)
'her cats regularly departed after snake's' is the wordplay.
'regularly departed' means one should take alternating letters (letters removed at regular intervals).
'after' means one lot of letters go next to another.
'snake' becomes 'asp' (asp is a kind of snake).
'her'+'cats'='hercats'
The alternate letters of 'hercats' are 'ect'.
'ect' put after 'asp' is 'ASPECT'.
(Other definitions for aspect that I've seen before include "front" , "Vista, panorama" , "The way something looks" , "'Scene, view, vista (6)'" , "Viewpoint, feature to be considered" .)