Baby's left a wet blanket (10)
I believe the answer is:
spoilsport
'a wet blanket' is the definition.
('spoilsport' can be a synonym of 'wet blanket')
'baby's left' is the wordplay.
'baby's' becomes 'spoils' (I can't explain this - if you can you should give a lot more credence to this answer).
'left' becomes 'port' (left side of a ship - opposite of starboard).
'spoils'+'port'='SPOILSPORT'
Can you help me to learn more?
(Other definitions for spoilsport that I've seen before include "Party pooper" , "One who ruins others' enjoyment" , "Person marring others' pleasure" , "One who reduces others' pleasure" , "One marring others' pleasure" .)