After renovation, their bars had a very tight margin … (5,7)
I believe the answer is:
hairs breadth
'a very tight margin' is the definition.
'after renovation their bars had' is the subsidiary indication.
'after renovation' indicates an anagram.
'their'+'bars'+'had'='theirbarshad'
'theirbarshad' with letters rearranged gives 'hairsbreadth'.
(Other definitions for hairs breadth that I've seen before include "little difference" , "by which Damocles escaped death?" , "tiny a distance" , "short distance" , "Narrow margin" .)