Grant access to the first miner through the entrance (5)
I believe the answer is:
admit
'grant access to' is the definition.
(I've seen this in another clue)
'first miner through the entrance' is the wordplay.
'first miner' becomes 'm' (1st letter of 'miner').
'through' indicates putting letters inside (inserted letters go through the word).
'the entrance' becomes 'adit' (I've seen this in another clue).
'm' placed inside 'adit' is 'ADMIT'.
'the' is the link.
(Other definitions for admit that I've seen before include "Take on" , "Profess" , "Usher in" , "receive" , "Stop being obstructive" .)