Soak one’s hair at first — it’s fairly excessive (8)
I believe the answer is:
steepish
'fairly excessive' is the definition.
(steep can mean costly or excessive)
'soak one's hair at first' is the wordplay.
'soak' becomes 'steep' (steeping is a kind of soaking).
'one's' becomes 'is' (Roman numeral).
'at first' says to take the initial letters.
The initial letter of 'hair' is 'h'.
'steep'+'is'+'h'='STEEPISH'
'it's' is the link.
(Other definitions for steepish that I've seen before include "Rather expensive" , "Quite expensive" , "Rather stiff" .)