Importance of mine host, initially (4)
I believe the answer is:
pith
'importance' is the definition.
(I've seen this in another clue)
'mine host initially' is the wordplay.
'mine' becomes 'pit' (as in a mining pit).
'initially' suggests taking the first letters.
The first letter of 'host' is 'h'.
'pit'+'h'='PITH'
'of' is the link.
(Other definitions for pith that I've seen before include "Orange product" , "Inside skin of, say, orange" , "Core - essence" , "Soft tissue; essence" , "Tissue beneath citrus fruit rind" .)