Delete Times puzzle finally (5)
I believe the answer is:
erase
'delete' is the definition.
(erasing is a kind of deleting)
'times puzzle finally' is the wordplay.
'times' becomes 'eras' (era is a kind of time).
'finally' indicates one should take the final letters.
The final letter of 'puzzle' is 'e'.
'eras'+'e'='ERASE'
(Other definitions for erase that I've seen before include "Scratch" , "Remove from memory" , "Do away with" , "score" , "Blank out" .)