Possessing will, still, to gather animals up (7)

'possessing will' is the definition.
(state of having had a will written up)

'still to gather animals up' is the wordplay.
'still' becomes 'yet' (yet can mean still or so far).
'to gather' indicates putting letters inside.
'animals' becomes 'cats' (cats are animals).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'yet' going around 'cats' is 'ycatset'.
'ycatset' back-to-front is 'TESTACY'.