Cries "Absolutely!," embracing Lord Lieutenant (5)
I believe the answer is:
yells
'cries' is the definition.
('yell' can be a synonym of 'cry')
'absolutely embracing lord lieutenant' is the wordplay.
'absolutely' becomes 'yes' (both can be used to give an affirmative answer).
'embracing' means one lot of letters goes inside another.
'lord lieutenant' becomes 'll' (this could be a standard abbreviation I've not previously seen).
'yes' enclosing 'll' is 'YELLS'.
Can you help me to learn more?
(Other definitions for yells that I've seen before include "Shouts loudly" , "Screams" , "Cries out" .)