Kelvin, terribly ill-bred, having run in; cross words? (4,5)

'cross words?' is the definition.
(set of words used when crossing a road)

'kelvin terribly ill-bred having run' is the wordplay.
'kelvin' becomes 'K' (abbreviation for the unit of temperature).
'terribly' indicates an anagram.
'having' means one lot of letters go next to another.
'run' becomes 'r' (cricket abbreviation).
'ill'+'bred'+'r'='illbredr'
'illbredr' anagrammed gives 'erbdrill'.
'k'+'erbdrill'='KERB DRILL'

'in' is the link.