Choose possession of miner, say (4)
I believe the answer is:
pick
I believe this clue is a double definition.
'choose' is the first definition.
(I know this)
'possession of miner say' is the second definition.
(a miner might use a pick)
(Other definitions for pick that I've seen before include "Play guitar" , "Choose - best" , "Pluck" , "Selection" , "Select - ground-breaking tool" .)