Group has right to my last drink (6)
I believe the answer is:
brandy
'last drink' is the definition.
'brandy' can be an answer for 'drink' (I've seen this in another clue). I am not sure about the 'last' bit.
'group has right to my' is the wordplay.
'group' becomes 'band' (band can mean a group of people).
'has' indicates putting letters inside.
'right' becomes 'r' (common abbreviation).
'to my' becomes 'y' (I can't justify this - if you can you should give a lot more credence to this answer).
'band' going around 'r' is 'brand'.
'brand'+'y'='BRANDY'
Can you help me to learn more?
(Other definitions for brandy that I've seen before include "Strong drink distilled from wine" , "warmer?" , "- - -snap" , "Grape wine spirit" , "Cognac is a well-known one" .)