Moderate old gallery contains space for all to see (9)
I believe the answer is:
extenuate
'moderate' is the definition.
(thesaurus)
'old gallery contains space for all to see' is the wordplay.
'old' becomes 'ex' (prefix meaning former or onetime).
'gallery' becomes 'tate' (Tate Modern, Tate Britain etc).
'contains' means one lot of letters goes inside another.
'space' becomes 'en' (in printing, a space as wide as a letter 'n').
'for all to see' becomes 'u' (universal dvd certificate).
'en'+'u'='enu'
'tate' placed around 'enu' is 'tenuate'.
'ex'+'tenuate'='EXTENUATE'
(Other definitions for extenuate that I've seen before include "Mitigate" , "Lessen the seriousness of (an offence) with a mitigating factor" .)