Hundreds of runs etc — strangely, that's admitted (9)
I believe the answer is:
centuries
'hundreds' is the definition.
('century' can be a synonym of 'hundred')
'runs etc strangely that's admitted' is the wordplay.
'strangely' is an anagram indicator.
'that's' becomes 'ie'.
'admitted' means one lot of letters goes inside another (inserted letters are admitted in).
'runs'+'etc'='runsetc'
'runsetc' is an anagram of 'centurs'.
'centurs' enclosing 'ie' is 'CENTURIES'.
'of' is the link.
(Other definitions for centuries that I've seen before include "Censure it for hundreds of years" , "Periods of 100 years" .)