Airless, exhausted, cold, finish climb (6)
I believe the answer is:
ascend
'climb' is the definition.
(climb can mean to ascend or go up)
'airless exhausted cold finish' is the wordplay.
'exhausted' says to hollow out the word (remove centre letters) (the word is emptied out or exhausted).
'cold' becomes 'C' (eg on taps).
'finish' becomes 'end' (come to an end).
'airless' with its centre taken out is 'as'.
'as'+'c'+'end'='ASCEND'
(Other definitions for ascend that I've seen before include "Travel upwards" , "Move upwards" , "Gain altitude" , "Move upward" , "Come up" .)