Care for a drink? Willingly! (4,1,4)
I believe the answer is:
like a shot
'willingly' is the definition.
(to do something like a shot is to do it willingly)
'care for a drink?' is the wordplay.
'care' becomes 'like' (synonyms).
'for a drink?' becomes 'ashot' (I can't justify this - if you can you should give a lot more credence to this answer).
'like'+'ashot'='LIKE A SHOT'
Can you help me to learn more?
(Other definitions for like a shot that I've seen before include "enthusiastically?" , "Enjoy a wee dram" , "What spirit drinkers do" , "sluggish?" , "straightaway?" .)