Former Queen Mother running inside (7)
I believe the answer is:
quondam
'former' is the definition.
(synonyms)
'queen mother running inside' is the wordplay.
'queen' becomes 'qu' (abbreviation for queen).
'mother' becomes 'dam' (female parent of an animal).
'running' becomes 'on' (I've seen this in other clues).
'inside' means one lot of letters goes inside another.
'qu'+'dam'='qudam'
'qudam' enclosing 'on' is 'QUONDAM'.
(Other definitions for quondam that I've seen before include "Former (Latin) - man quod (anag)" , "Erstwhile" .)