Royal family starts grumbling (4)
I believe the answer is:
king
'royal' is the definition.
(a king is royal)
'family starts grumbling' is the wordplay.
'family' becomes 'kin' (synonyms).
'starts' says to take the initial letters.
The first letter of 'grumbling' is 'g'.
'kin'+'g'='KING'
(Other definitions for king that I've seen before include "Playing card" , "indispensable on board" , "Honour for man" , "Most important chessman" , "Mythical monarch commemorated by 1" .)