Who did Agamemnon leave to look after Clytemnestra? How did Aegisthus get rid of him

A bard. Aegisthus basically killed the bard.

Explanation:

"There was a bard with her, to whom Agamemnon had given strict orders on setting out for Troy, that he was to keep guard over his wife; ". Agamemnon gave orders to a serving person, probably a storyteller or singer.

Aegisthus carried this bard off to a desert island and left him there for crows and seagulls to batten upon