Importance of mine host, originally (4)
I believe the answer is:
pith
'importance' is the definition.
(I've seen this in another clue)
'mine host originally' is the wordplay.
'mine' becomes 'pit' (down the pit).
'originally' indicates taking the first letters.
The first letter of 'host' is 'h'.
'pit'+'h'='PITH'
'of' acts as a link.
(Other definitions for pith that I've seen before include "nub of matter" , "Lining of rind; essence" , "Medulla" , "Spongy tissue like that lining an orange skin" , "The white part of the orange" .)