Long walk on an empty track round the centre of Florence (4)
I believe the answer is:
trek
'long walk' is the definition.
(I've seen this in another clue)
'an empty track round the centre of florence' is the wordplay.
'an empty' suggests removing the centre.
'round' indicates putting letters inside.
'the centre of' means to look at the middle letters.
'track' with its middle taken out is 'tk'.
The middle letters of 'florence' are 're'.
'tk' going around 're' is 'TREK'.
'on' acts as a link.
(Other definitions for trek that I've seen before include "Long and difficult trip" , "Expedition or difficult trip" , "Great journey" , "A long arduous journey as in S Africa" , "A long hard march" .)