A half bottle contains a very big encouragement (5)
I believe the answer is:
boost
'encouragement' is the definition.
(I know that encouragement can be written as boost)
'a half bottle contains a very big' is the wordplay.
'a half' suggests halving the letters.
'contains' means one lot of letters goes inside another.
'a very big' becomes 'os' (abbreviation for outsize).
'bottle' with half the letters taken is 'bot'.
'bot' going around 'os' is 'BOOST'.
(Other definitions for boost that I've seen before include "Fillip" , "promotion" , "Help to increase" , "Increase (strength or morale)" , "Uplift" .)