Number perhaps close enough? (5)
I believe the answer is:
local
This clue is a double definition.
'number' is the first definition.
(local local anaesthetic is a type of 'numb-er')
'close enough?' is the second definition.
'perhaps' acts as a link.
(Other definitions for local that I've seen before include "Neighbourhood pub or resident" , "Near at hand" , "In nearby area" , "Your friendly neighbourhood pub" , "bar" .)