Give an exclamation and run after him (6)

I believe the answer is:
horace
'him' is the definition.
'give an exclamation and run after' is the wordplay.
'give an' becomes 'h' (I can't explain this - if you can you should give a lot more credence to this answer).
'exclamation' becomes 'o'.
'and' is a charade indicator (letters next to each other).
'run' becomes 'race' (synonyms).
'after' means one lot of letters go next to another.
'h'+'o'+'race'='HORACE'
Can you help me to learn more?
(Other definitions for horace that I've seen before include "Roman poet and satirist" , "Latin ode writer" , "- Walpole, eighteenth century English author" , "Odist" , "Roman poet; -- Walpole" .)
