Right-hand man keeps to speaking well (8)
I believe the answer is:
rhetoric
'speaking well' is the definition.
'rhetoric' can be an answer for 'speaking' (thesaurus). I am not certain of the 'well' bit.
'right-hand man keeps to' is the wordplay.
'right hand' becomes 'RH' (abbreviation).
'man' becomes 'eric' (I've seen this before).
'keeps' is an insertion indicator (inserted letters are kept inside).
'eric' going around 'to' is 'etoric'.
'rh'+'etoric'='RHETORIC'
Can you help me to learn more?
(Other definitions for rhetoric that I've seen before include "Persuasive speech" , "Art of impressive public speaking" , "Effective or persuasive language" , "Hot air -- rich rote (anag)" , "address" .)