Block of limestone pavement, stone, cold for feet, initially (5)
I believe the answer is:
clint
'block of limestone pavement' is the definition.
'cold for feet initially' is the wordplay.
'cold' becomes 'c' (eg on taps).
'for' means one lot of letters go next to another.
'feet initially' becomes 'lint' (I am not sure about this - if you are sure you should believe this answer much more).
'c'+'lint'='CLINT'
'stone' is the link.
I am not very happy about this link. It may belong to another bit of the clue.
(Another definition for clint that I've seen is " -- Eastwood, actor".)