Waste beginning to deter Arctic explorer (5)
I believe the answer is:
dross
'waste' is the definition.
(dross is a kind of waste)
'beginning to deter arctic explorer' is the wordplay.
'beginning to' suggests taking the first letters.
'arctic explorer' becomes 'ross' (John Ross).
The first letter of 'deter' is 'd'.
'd'+'ross'='DROSS'
(Other definitions for dross that I've seen before include "Lees" , "Scum on molten metals" , "Rubbish, scum" , "Slag!" , "Anything worthless" .)