Company head’s rigidity (8)
I believe the answer is:
firmness
'rigidity' is the definition.
(I've seen this before)
'company head's' is the wordplay.
'company' becomes 'firm' (I've seen this before).
'head' becomes 'ness' (ness is a headland).
'firm'+'ness'='FIRMNESS'
(Other definitions for firmness that I've seen before include "Rigidity" , "Solidity" , "Strength of will" , "Resolution" .)