At first cat, then a dog, beside one tree or another (8)
I believe the answer is:
calabash
'or another' is the definition.
I can't tell whether this defines the answer.
'at first cat then a dog beside one tree' is the wordplay.
'at first' indicates taking the first letters.
'then' is a charade indicator (letters next to each other).
'dog' becomes 'lab' (short for labrador).
'beside' means one lot of letters go next to another (I've seen this in other clues).
'one tree' becomes 'ash' (ash is a kind of tree).
The first letter of 'cat' is 'c'.
'c'+'a'+'lab'+'ash'='CALABASH'
(Other definitions for calabash that I've seen before include "water-container" , "Tree with hard-shelled fruit" , "Tropical evergreen tree, might lash a cab, oddly" , "Bottle gourd" , "Large, hard-shelled fruit" .)