Runs into stone at the beginning (4)
I believe the answer is:
germ
'the beginning' is the definition.
(germ is a kind of beginning)
'runs into stone' is the wordplay.
'runs' becomes 'r' (cricket abbreviation).
'into' means one lot of letters goes inside another.
'stone' becomes 'gem' (I've seen this before**).
'r' put into 'gem' is 'GERM'.
'at' is the link.
(Other definitions for germ that I've seen before include "First idea; seed embryo" , "Beginning (of an idea?)" , "Minute lifeform" , "Cause of illness" , "Infectious microorganism" .)