Used to be very little around the tourist centre (4)
I believe the answer is:
were
'used to be' is the definition.
(eg 'you were...' means 'you used to be...')
'little around the tourist centre' is the wordplay.
'little' becomes 'wee' (similar in meaning).
'around' is an insertion indicator.
'centre' says to take the centre.
The central letter of 'tourist' is 'r'.
'wee' enclosing 'r' is 'WERE'.
'very' is the link.
(Other definitions for were that I've seen before include "Used to be" , "Lycanthrope" , "Existed in the past" , "(We/you) existed" , "(You/we/they) existed" .)