Think about taking me round the States (4)
I believe the answer is:
muse
'think about' is the definition.
(thesaurus)
'me round the states' is the wordplay.
'round' means one lot of letters goes inside another.
'the states' becomes 'US' (abbreviation for the United States).
'me' enclosing 'us' is 'MUSE'.
'taking' is the link.
(Other definitions for muse that I've seen before include "Source of inspiration; rock group" , "Goddess; rock group" , "Source of artistic inspiration" , "Meditate on a goddess of the arts" , "Ponder or meditate" .)