That of a monarch with only half a domain? (7)
I believe the answer is:
kingdom
'that of a' is the definition.
I can't tell whether this definition defines the answer.
'monarch with only half a domain?' is the wordplay.
'monarch' becomes 'king' (king is a kind of monarch).
'with' is a charade indicator (letters next to each other).
'only half' indicates taking half.
'domain' halved is 'dom'.
'king'+'dom'='KINGDOM'
Can you help me to learn more?
(Other definitions for kingdom that I've seen before include "Regal realm" , "All the animals" , "Republic? Not so!" , "What Richard III would have given for a horse" , "Country with royal head of state" .)