A friend to pass the time with (4,4)

'time with' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'a friend to pass' is the wordplay.
'a friend' becomes 'mate' (mate is a kind of friend).
'to' is a charade indicator (letters next to each other) (I've seen this in other clues).
'pass' becomes 'cell' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'mate' put after 'cell' is 'CELL MATE'.

'the' acts as a link.

Can you help me to learn more?