Inflexible, strict (4,3,4)
I believe the answer is:
hard and fast
I believe this is a double definition.
'inflexible' is the first definition.
(I've seen this before)
'strict' is the second definition.
(I know that strict can be written as hard-and-fast)
(Other definitions for hard and fast that I've seen before include "(Of rules) invariable" , "Strict" , "Stupid person" , "like a cannonball" , "Not moving" .)