Looked after grave first, being of solemn demeanour (7-6)
I believe the answer is:
serious-minded
'first being of solemn demeanour' is the definition.
I don't know anything about this answer so I cannot judge whether this works.
'looked after grave' is the wordplay.
I cannot really understand how this works, but
'grave' could be 'serious' (synonyms) and 'serious' is located in the answer.
'looked after' could be 'minded' (I've seen this in another clue) and 'minded' is present in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
I've seen this clue in The Daily Express.
Want a hint initially instead of a full solution?
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