Keen to get a six on top of die (4)
I believe the answer is:
avid
'keen' is the definition.
(both can mean enthusiastic)
'a six on top of die' is the wordplay.
'six' becomes 'VI' (Roman numerals).
'on top of' suggests taking the first letters.
The first letter of 'die' is 'd'.
'a'+'vi'+'d'='AVID'
'to get' acts as a link.
(Other definitions for avid that I've seen before include "'Eager, enthusiastic (4)'" , "Greedy like diva" , "deeply enthusiastic" , "Greedily eager" , "Zealous, enthusiastic" .)