Drink beginning to cheer up dad (5)
I believe the answer is:
cuppa
'drink' is the definition.
(cuppa is a kind of drink)
'beginning to cheer up dad' is the wordplay.
'beginning to' suggests taking the first letters.
'dad' becomes 'pa' (both can mean one's father).
The initial letter of 'cheer' is 'c'.
'c'+'up'+'pa'='CUPPA'
(Other definitions for cuppa that I've seen before include "Refreshing brew" , "Drink of tea (informal)" , "Drink of tea (colloq.)" .)