Military policeman following me to his place in Tennessee (7)
I believe the answer is:
memphis
'in tennessee' is the definition.
('Memphis' is part of 'tennessee')
'military policeman following me to his' is the wordplay.
'military policeman' becomes 'MP' (synonyms).
'following' means one lot of letters go next to another.
'mp' after 'me' is 'memp'.
'memp'+'his'='MEMPHIS'
'place' acts as a link.
(Other definitions for memphis that I've seen before include "US city where Gracelands is located" , "City of Tennessee/Egypt" , "Largest city in Tennessee" , "Ancient Egyptian city" , "Name of city at different times overlooking the Nile and Mississippi?" .)