Statesman each day left time to track ancient Chester (5,2,6)

'statesman' is the definition.
(I know that Eamon de Valera is a statesman)

'each day left time to track ancient chester' is the wordplay.
I cannot really understand how this works, but
'each' could be 'ea' (abbreviation) and 'ea' is found in the answer.
'day' could be 'mon' (short for Monday) and 'mon' is present in the answer.
'left' could be 'l' (common abbreviation) and 'l' is located in the answer.
'time' could be 'era' (an era is a period of time) and 'era' is located in the answer.
The remaining letters 'deva' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?