Drifting, veteran explorer's beginning to weaken (8)
I believe the answer is:
enervate
'weaken' is the definition.
(I know that enervate is a more specific form of the action the weaken)
'drifting veteran explorer's beginning' is the wordplay.
'drifting' indicates an anagram.
'beginning' suggests taking the first letters.
The initial letter of 'explorers' is 'e'.
'veteran' is an anagram of 'enervat'.
'enervat'+'e'='ENERVATE'
'to' is the link.
(Other definitions for enervate that I've seen before include "Make drained of energy" , "Spiritless" , "Make weak" , "Unnerve, unsettle" , "Weaken mentally or morally" .)