Supposing you turn up at the party with a dog (4)
I believe the answer is:
fido
'dog' is the definition.
(I know that Fido is a dog)
'supposing you turn up at the party' is the wordplay.
'supposing you' becomes 'if' (I can't explain this - if you can you should believe this answer much more).
'turn up' says the letters should be written in reverse.
'at' is a charade indicator (letters next to each other).
'the party' becomes 'do' (do can informally mean a party).
'if' reversed gives 'fi'.
'fi'+'do'='FIDO'
'with a' acts as a link.
Can you help me to learn more?
(Other definitions for fido that I've seen before include "Fog disperser" , "it would disperse fog" , "Typical dog's name" , "Dog perhaps" .)