Plodded into the Home Counties and moved on apace (6)
I believe the answer is:
strode
'moved on apace' is the definition.
(to stride is to move quickly)
'plodded into the home counties' is the wordplay.
'plodded' becomes 'trod'.
'into' indicates putting letters inside.
'the home counties' becomes 'se' (Home Counties in the South East of England).
'trod' placed within 'se' is 'STRODE'.
'and' is the link.
(Other definitions for strode that I've seen before include "Walked fast with long steps" , "Galumphed" , "Paced" , "went on foot" .)