Tries to take a girl around central Tooting (5)
I believe the answer is:
tests
'tries' is the definition.
('test' can be a synonym of 'try')
'a girl around central tooting' is the wordplay.
'a girl' becomes 'tess' (girl's name).
'around' is an insertion indicator.
'central' indicates the central letters.
The central letter of 'tooting' is 't'.
'tess' enclosing 't' is 'TESTS'.
'to take' is the link.
(Other definitions for tests that I've seen before include "Trials -- tribulations" , "Critically examines" , "Trials, exams" , "Trials for cricketers" , "Puts to proof at cricket matches" .)