Man possibly absorbing first of this fibre (5)
I believe the answer is:
istle
'fibre' is the definition.
(I've seen this before)
'man possibly absorbing first of this' is the wordplay.
'man possibly' becomes 'isle' (Isle of Man is an example).
'absorbing' means one lot of letters goes inside another.
'first of this' becomes 't' (1st letter of 'this').
'isle' enclosing 't' is 'ISTLE'.
(Other definitions for istle that I've seen before include "for making nets?" , "Carpet material" , "Fibre from yucca or agave trees" .)