Steady head of industry lies about following attempt (9)
I believe the answer is:
stabilise
'steady' is the definition.
(I know that steady can be written as stabilise)
'head of industry lies about following attempt' is the wordplay.
'head of' suggests taking the first letters.
'about' indicates anagramming the letters.
'following' is a charade indicator (letters next to each other).
'attempt' becomes 'stab' (to have a stab is to attempt something).
The initial letter of 'industry' is 'i'.
'lies' anagrammed gives 'lise'.
'i'+'lise'='ilise'
'ilise' after 'stab' is 'STABILISE'.
(Other definitions for stabilise that I've seen before include "get on an even keel" , "Put into an equilibrium" , "Make firm" , "Make of keep steady or balanced" , "Become less changeable" .)