Fighting to get hold of iron that’s very thin (5)
I believe the answer is:
wafer
'very thin' is the definition.
('wafer thin' means very thin)
'fighting to get hold of iron' is the wordplay.
'fighting' becomes 'war'.
'to get hold of' indicates putting letters inside.
'iron' becomes 'Fe' (Fe is the chemical symbol for iron).
'war' placed around 'fe' is 'WAFER'.
'that's' is the link.
(Other definitions for wafer that I've seen before include "Thin, crisp biscuit or bread" , "Thin type" , "Ice cream's biscuit" , "Host's" , "Ice cream biscuit" .)